If A is a square matrix such that A² = I, then find the simplified value of (A-I)³+(A+I)³-7A.

Without expanding evaluate the determinant\(\left| \begin{matrix} sin\alpha & cos\alpha & sin(\alpha +\delta ) \\ sin\beta & cos\beta & sin(\beta +\delta ) \\ sin\gamma & cos\gamma & sin(\gamma +\delta ) \end{matrix} \right| \)

Find the equation of the line joining A(1,3) and B(0,0) using determinants and find k if D(k,0) is a point such that area of \(\triangle\)ABC is 3 sq. units.

If \(A=\left[ \begin{matrix} 2 & 3 \\ 4 & 5 \end{matrix} \right] \) find A² - 7A - 21.

If \(A=\left[ \begin{matrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{matrix} \right] \), Show that k so that A² -4A- 51 = 0