Q7. Consider the square matrices
$A = \begin{bmatrix} 3 & 5 \\ 2 & 3 \end{bmatrix}$, $O = \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$, and $B = \begin{bmatrix} A & A^2 \\ O & A \end{bmatrix}$.
Use block matrices to find, a) $B^{-1}$. b) det$(B)$.
Note: For $A = \begin{bmatrix} A_1 & A_2 \\ O & A_3 \end{bmatrix}$, $A^{-1} = \begin{bmatrix} A_1^{-1} & -A_1^{-1}A_2A_3^{-1} \\ 0 & A_3^{-1} \end{bmatrix}$ and det$(A) = $det$(A_1)$det$(A_3)$
