If $|\operatorname{Adj} A|=x$ and $|\operatorname{Adj} B|=y$, then $\left|(\operatorname{Adj}(AB))^{-1}\right|=$

If $A = \begin{bmatrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix}$ and $A \cdot \text{adj}(A) = \begin{bmatrix} k & 0 \\ 0 & k \end{bmatrix}$,then $k$ is equal to

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

Find the inverse of the matrix $A = \left[\begin{array}{ll}2 & 5 \\ 1 & 3\end{array}\right]$,if it exists.

Let $A = \begin{bmatrix} 1 & -2 & 1 \\ -2 & 3 & 1 \\ 1 & 1 & 5 \end{bmatrix}$. Verify that $[adj A]^{-1} = adj(A^{-1})$.

If matrix $A = \frac{1}{11} \begin{bmatrix} -1 & 7 & -24 \\ 2 & a & 4 \\ 2 & -3 & 15 \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} 3 & 3 & 4 \\ 2 & -3 & 4 \\ b & -1 & c \end{bmatrix}$,then the values of $a, b, c$ respectively are ......