If A = \(\left[ \begin{matrix} 8 & -6 & 2 \\ -6 & 7 & -4 \\ 2 & -4 & 3 \end{matrix} \right] \), verify thatA(adj A) = (adj A)A = |A| I₃.

If A = \(\left[ \begin{matrix} 4 & 3 \\ 2 & 5 \end{matrix} \right] \), find x and y such that A² + xA + yI₂ = O₂. Hence, find A^-1.

If A = \(\frac { 1 }{ 7 } \left[ \begin{matrix} 6 & -3 & a \\ b & -2 & 6 \\ 2 & c & 3 \end{matrix} \right] \) is orthogonal, find a, b and c , and hence A⁻¹.

If F(\(\alpha\)) = \(\left[ \begin{matrix} \cos { \alpha } & 0 & \sin { \alpha } \\ 0 & 1 & 0 \\ -\sin { \alpha } & 0 & \cos { \alpha } \end{matrix} \right] \), show that [F(\(\alpha\))]^-1 = F(-\(\alpha\)).

If A = \(\left[ \begin{matrix} 5 & 3 \\ -1 & -2 \end{matrix} \right] \), show that A² - 3A - 7I₂ = O₂. Hence find A⁻¹.