If \(A=\left[\begin{array}{lll}2 & -3 & 4\end{array}\right], B=\left[\begin{array}{l}3 \\ 2 \\ 2\end{array}\right], X=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]\) and \(Y=\left[\begin{array}{l}2 \\ 3 \\ 4\end{array}\right]\), then AB+XY is equal to

Given that matrices A and B are of order \(3 \times n\) and \(m \times 5\) respectively, then the order of matrix C = 5A + 3B is

Given that \(A=\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha\end{array}\right]\) and \(A^2=3 I\), then

If A is a square matrix such that A²=A, then (I + A)³ – 7A is

If \(A=\left[\begin{array}{cc}0 & 2 \\ 3 & -4\end{array}\right]\) and \(k A=\left[\begin{array}{cc}0 & 3 a \\ 2 b & 24\end{array}\right]\), then the value of k, a and b respectively, are

A matrix \(A=\left[a_{i j}\right]_{3 \times 3}\) is defined by \(a_{i j}=\left\{\begin{array}{cl}2 i+3 j, & i<j \\ 5, & i=j . \\ 3 i-2 j, & i>j\end{array}\right.\) The number of elements in A which are more than 5 , is

If \(\left[\begin{array}{cc}2 a+b & a-2 b \\ 5 c-d & 4 c+3 d\end{array}\right]=\left[\begin{array}{cc}4 & -3 \\ 11 & 24\end{array}\right]\), then the value of a+b-c+2d is

If \(A=\left[a_{i j}\right]\) is a square matrix of order 2 such that \(a_{i j}=\left\{\begin{array}{ll}1, & \text { when } i \neq j \\ 0, & \text { when } i=j\end{array}\right.\), then \(A^2\) is

If \(A=\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right], B=\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]\) and \(A=B^2\), then x equals

A and B are square matrices of same order. If (A+B)²= A² + B², then

If \(A=\left[\begin{array}{ll}3 & 4 \\ 5 & 2\end{array}\right]\) and 2 A+B is a null matrix, then B is equal to

If \(x\left[\begin{array}{l}1 \\ 2\end{array}\right]+y\left[\begin{array}{l}2 \\ 5\end{array}\right]=\left[\begin{array}{l}4 \\ 9\end{array}\right]\), then

If \(A=\left[\begin{array}{ll} x & 0 \\ 1 & 1 \end{array}\right]\) and \(B=\left[\begin{array}{cc} 4 & 0 \\ -1 & 1 \end{array}\right]\) then the value of x for which A² = B is

For the matrix A = \(\left[\begin{array}{ccc} 2 & -1 & 1 \\ \lambda & 2 & 0 \\ 1 & -2 & 3 \end{array}\right]\) to be invertible, the value of \(\lambda\) is

The product of matrix P and Q is equal to a diagonal matrix. If the order of matrix Q is 3 \(\times\) 2, then the order of matrix P is

lf A is a square matrix of order 2 and |A| = -2, then value of |5A'| is

Find the matrix A², where A = [a_ij] is a 2 \(\times\) 2 matrix whose elements are given by
a_ij = maximum (i, j) - minimum (i, j)

If [x 2 0] \(\left[\begin{array}{c} 5 \\ -1 \\ x \end{array}\right]\)=[3 1] \(\left[\begin{array}{c} -2 \\ x \end{array}\right]\), then value of x is

If inverse of matrix \(\left[\begin{array}{ccc} 7 & -3 & -3 \\ -1 & 1 & 0 \\ -1 & 0 & 1 \end{array}\right]\)is the matrix \(\left[\begin{array}{lll} 1 & 3 & 3 \\ 1 & \lambda & 3 \\ 1 & 3 & 4 \end{array}\right]\), then the value of \(\lambda\) is

If A is a square matrix of order 3 such that the value of | adj A | = 8, then the value of |4^T | is

If A = \(\left[\begin{array}{ccc} a & c & -1 \\ b & 0 & 5 \\ 1 & -5 & 0 \end{array}\right]\) is a skew-symmetric matrix, then the value of 2a - (b + c) is

If \(A=\left[\begin{array}{ll} 3 & -2 \\ 4 & -2 \end{array}\right]\) then the value of kif, A² = kA - 2I is

The matrix \(\left[\begin{array}{rrr} 2 & -1 & 4 \\ 1 & 0 & -5 \\ -4 & 5 & 7 \end{array}\right]\) is

If matrix A is of order m x n, and for matrix B, AB and BA both are defined, then order of matrix B is

A matrix has 18 elements, then possible number of orders of a matrix are

If \(A=\left[\begin{array}{rr} 3 & 1 \\ -1 & 2 \end{array}\right]\) then A² - 5A - 7I iS

If \(A=\left[\begin{array}{lll} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array}\right]\) then A⁶ is equal to

The matrix A satisfies the equation \(\left[\begin{array}{rr} 0 & 2 \\ -1 & 1 \end{array}\right] A=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]\) then matrix A is

If \(F(x)=\left[\begin{array}{rr} \cos x & \sin x \\ -\sin x & \cos x \end{array}\right] \text { , }\) then F(x) F(y) is equal to

If A and B are symmetric matrices of same order, then (AB' - BA') is a

For any two matrices A and B, we have

The value of x such that
\(\left[\begin{array}{lll} 1 & 2 & 1 \end{array}\right]\left[\begin{array}{lll} 1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2 \end{array}\right]\left[\begin{array}{l} 0 \\ 2 \\ x \end{array}\right]=O, \mathrm{i}\)
 

If matrix \(A=\left[a_{i j}\right]_{2 \times 2},\ where \ a_{i j}=\left\{\begin{array}{l}1, \text { if } i \neq j \\ 0, \text { if } i=j\end{array}\right.\) Then \(A^{2}\) is equal to 

 If \(\left[\begin{array}{cc}2 x+y & 4 x \\ 5 x-7 & 4 x\end{array}\right]=\left[\begin{array}{cc}7 & 7 y-13 \\ y & x+6\end{array}\right]\), then

If A and B are square matrices of the same order and AB = 3I,then A^-1 is equal to

Matrices A and B will be inverse of each other only if

If X, A and B are matrices of the same order such that X = AB, then we apply elementary row transformations simultaneously on X and on the matrix

On using elementary row operation \(R_{1} \rightarrow R_{1}-3 R_{2}\) in the following matrix equation \(\left[\begin{array}{ll}4 & 2 \\ 3 & 3\end{array}\right]=\left[\begin{array}{ll}1 & 2 \\ 0 & 3\end{array}\right]\left[\begin{array}{ll}2 & 0 \\ 1 & 1\end{array}\right],\) we have

On using elementary column operations \(C_{2} \rightarrow C_{2}-2 C_{1}\) in the following matrix equation \(\left[\begin{array}{cc}1 & -3 \\ 2 & 4\end{array}\right]=\left[\begin{array}{cc}1 & -1 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}3 & 1 \\ 2 & 4\end{array}\right]\), we have

On usiig elementary column operations C₂➝ C₂ - 2C₁ in the following matrix equation\(\left[\begin{array}{cc} 1 & -3 \\ 2 & 4 \end{array}\right]=\left[\begin{array}{cc} 1 & -1 \\ 0 & 1 \end{array}\right]\left[\begin{array}{cc} 3 & 1 \\ 2 & 4 \end{array}\right]\) ,we have 

The matrix \(\left[\begin{array}{ccc}0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0\end{array}\right]\) is a

\(A=\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]\), then if the value of \(\alpha\) is

The set of all 2x 2 matrices which is commutative with the matrix.\(\left[\begin{array}{ll} 1 & 1 \\ 1 & 0 \end{array}\right]\) with respect to matrix multiplication is

If A and B are square matrices of the sameorder, then (A + B) (A - B) is equal to

If \(A=\left[\begin{array}{ccc} 2 & -1 & 3 \\ -4 & 5 & 1 \end{array}\right] \text { and } B=\left[\begin{array}{cc} 2 & 3 \\ 4 & -2 \\ 1 & 5 \end{array}\right] \text { , then }\) 

If the product of two matrices is a zero matrix, then

The product \(\left[\begin{array}{rr} a & b \\ -b & a \end{array}\right]\left[\begin{array}{rr} a & -b \\ b & a \end{array}\right]\) is equal to

If A and B are two matrices of the order \(3 \times m\) and \(3 \times n\) respectively and m=n, then the order of the matrix \((5 A-2 B)\) is 

If \(\left[\begin{array}{rr}1 & 2 \\ -2 & -b\end{array}\right]+\left[\begin{array}{ll}a & 4 \\ 3 & 2\end{array}\right]=\left[\begin{array}{ll}5 & 6 \\ 1 & 0\end{array}\right]\), then \(a^{2}+b^{2}\) is equal to

1f If \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right], B=\left[\begin{array}{lll}1 & 3 & 2 \\ 4 & 3 & 1\end{array}\right], C=\left[\begin{array}{l}1 \\ 2\end{array}\right]\) and \(D=\left[\begin{array}{lll}4 & 6 & 8 \\ 5 & 7 & 9\end{array}\right]\), then which of the following is defined?

Which of the given values of x and y make the following pair of matrices equal \(\left[\begin{array}{cc} 3 x+7 & 5 \\ y+1 & 2-3 x \end{array}\right]\left[\begin{array}{cc} 0 & y-2 \\ 8 & 4 \end{array}\right] ?\)

The matrix \(P=\left[\begin{array}{lll} 0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0 \end{array}\right]\) is not A.

Total number of possible matrices of order 3 x 3 with each entry 2 or 0 is

If a matrix has 8 elements, then which of the following will not be a possible order of the matrix?

If A is a 3 x 2 matrix, B is a 3 x 3 matrix and Cis a 2 x 3 matrix, then the elements in A, Band C are respectively

 To construct a 2 x 3 matrix [a_ij], such that aij = – \(\frac { i-3j }{ 4 } \) The values that i and j can take are …….

If, \({ a }_{ ij }=\frac { 1 }{ 2 } |i-3j|\) the value of a₂₂ is

What is the element in the 2^nd row and 1^st column of a 2 x 2 Matrix A= [ a_ij], such that a = (i + 3) (j – 1)

\(\left[ \begin{matrix} 2 & 3 & 1 \\ 1 & 2 & 4 \end{matrix}\begin{matrix} 5 & 1 \\ 2 & 2 \end{matrix} \right] \) is a matrix of order

\(\begin{bmatrix} 3 & 0 \\ 0 & 4 \end{bmatrix}\) is example of 

Consider the following information regarding the number of men and women workers in three BPOs I, II and III

What does the entry in the second row and first column represent if the information is represented as a 3 x 2 matrix?

[5] is a scalar matrix of order

For what real value of y will matrix A be equal to matrix B, where
\(A=\begin{bmatrix} 3x-4 & 5y \\ 8 & { y }^{ 2 }-4y \end{bmatrix};B=\begin{bmatrix} x+1 & 6{ y }^{ 2 }+1 \\ 8 & -3 \end{bmatrix}\)

\(\begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix}\) is a matrix of order

\(\begin{bmatrix} x+10 & { y }^{ 2 }+2y \\ 0 & -4 \end{bmatrix} =\begin{bmatrix} 3x+4 & 3 \\ 0 & { y }^{ 2 }-5y \end{bmatrix}\) Then the value of x is ________

If A is square matrix such that A² = A, then (I + A)³ – 7 A is equal to

If the matrix A is both symmetric and skew symmetric, then

If A = \(\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}\) is such that A² = I, then

If A = \(\begin{bmatrix} cos\alpha & -sin\alpha \\ sin\alpha & cos\alpha \end{bmatrix}\), and A + A' = I, then the value of a is

Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k, respectively. 
If n = p, then the order of the matrix 7X – 5Z is:

Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k, respectively. 
The restriction on n, k and p so that PY + WY will be defined are:

The number of all possible matrices of order 3 × 3 with each entry

A = [a_ij]_{m × n\} is a square matrix, if

If A = \(\begin{bmatrix} 5 & x \\ y & 0 \end{bmatrix}\) and A = A’ then

The diagonal elements of a skew symmetric matrix are

If A = \(\begin{bmatrix} 0 & 2 \\ 2 & 0 \end{bmatrix}\)

If matrices A and B are inverse of each other then

 If A is a square matrix such that A²=A, then (I + A)² – 3A is

Total number of possible matrices of order 2 × 3 with each entry 1 or 0 is

 If A = diag(3, -1), then matrix A is

If A = [a_ij] is a 2 × 3 matrix, such that a_ij = \(\frac { { (-i+2j) }^{ 2 } }{ 5 }.\) Then a₂₃ is ________

If a matrix has 6 elements, then number of possible orders of the matrix can be

Assertion: Matrix \(\begin{bmatrix} 1& 0& 0\\ 0& 3& 0\\ 0& 0& 4\\ \end{bmatrix}\) is a diagonal matrix.
Reason: Identity matrix of order 3 is a diagonal matrix.
(a) Both A and R are correct; R is the correct explanation of A
(b) Both A and R are correct; R is not the correct explanation of A
(c) A is correct; R is incorrect
(d) R is correct; A is incorrect

Assertion: The matrix \(A=\begin{bmatrix} 9& 1& 2\\ 3& 7& 4\\ \end{bmatrix}\)does not possesses any inverse.
Reason: A is not a square matrix.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Assertion: The matrix \(A=\begin{bmatrix} 0& -1& -2\\ 1& 0& -3\\ 2& 3& 0\\ \end{bmatrix}\)is a skew symmetric matrix.
Reason: For the given matrix A we have A' = A.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Assertion: Let \(A=\begin{bmatrix} 1& 4\\ 2& 5\\ 4& 7\\ \end{bmatrix}\)and \(B=\begin{bmatrix} 4& 3& 6\\ 7& 8& 9\\ 5& 1& 2\\ \end{bmatrix}\), then the product of the matrices A and B is not defined.
Reason: The number of rows in B is not equal to number of columns in A.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Assertion: If A = \(\begin{bmatrix} 2& 3\\ 1& 2\\ \end{bmatrix}\)and B = \(\begin{bmatrix} 2& -3\\ -1& 2\\ \end{bmatrix}\), then B is the inverse of A.
Reason: If A is a square matrix of order m and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is called the inverse of A.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Assertion: \(\begin{bmatrix} 3& 0& 0\\ 0& 4& 0\\ 0& 0& 7\\ \end{bmatrix}\) is a diagonal matrix.
Reason: A = [a_ij] is a square matrix such that a_ij = 0, \(\forall i\neq j\),then A is called diagonal matrix. 
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

For any square matrix A with real number entries, consider the following statements.
Assertion: A  + A' is a symmetric matrix.
Reason: A - A' is a skew-symmetric matrix.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Assertion: If \( A=\frac{1}{3}\begin{bmatrix} 1& -2& 2\\ -2& 1& 2\\ -2& -2& -1\\ \end{bmatrix}\), then (A^T)A = I
Reason: For any square matrix, A(A^T)^T = A
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Assertion: Addition of matrices is an example of binary operation on the set of matrices of the same order.
Reason: Addition of matrix is commutative.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Assertion: The order of the matrix A is 3 x 5 and that of B is 2 x 3.Then the matrix AB is not possible.
Reason: No. of columns in A is not equal to no. of rows in B.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Assertion: The possible dimensions of a matrix containing 32 elements is 6.
Reason: The No. of ways of expressing 32 as a product of two positive integers is 6.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.