If $A = \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix}$,then $|A| |adj A|$ is equal to

Let $A$ be a $3 \times 3$ matrix and $B$ be its adjoint matrix. If $|B|=64,$ then $|A|$ is equal to

If $A = \begin{bmatrix} 2 & -3 \\ 5 & 4 \end{bmatrix}$,then $A^{-1} = $ . . . . . . .

Find the adjoint of the matrix: $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$

If $A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$ and $A \cdot \text{adj}(A) = A \cdot A^T$,then find the value of $5a + b$.

Let $F(\alpha ) = \begin{bmatrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{bmatrix}$,where $\alpha \in \mathbb{R}$. Then $[F(\alpha )]^{-1}$ is equal to