If $A = \begin{bmatrix} 1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1 \end{bmatrix}$ and $\text{adj } A = \begin{bmatrix} 5 & x & -2 \\ 1 & 1 & 0 \\ -2 & -2 & y \end{bmatrix}$,then the value of $x+y$ is:

If $A$ is a square matrix of order $3$,then consider the following statements.
$I$. If $|A|=0$,then $|\operatorname{Adj} A|=0$
$II$. If $|A| \neq 0$,then $|A^{-1}|=|A|^{-1}$
Which of the above statements is/are true?

If $P = \begin{vmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{vmatrix}$ is the adjoint of a $3 \times 3$ matrix $A$ and $\det(A) = 4$,then $\alpha$ is equal to

By using elementary operations,find the inverse of the matrix $A=\left[\begin{array}{rr}1 & 2 \\ 2 & -1\end{array}\right]$.

If $A$ is a square matrix of order $3$,then $|\operatorname{Adj}(\operatorname{Adj} A^2)|=$

Find the inverse of the matrix $\left[\begin{array}{cc}-1 & 5 \\ -3 & 2\end{array}\right]$ (if it exists).