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 $a, b, c$ and $d$ are real numbers such that $a^2+b^2+c^2+d^2=1$ and $A=\left[\begin{array}{cc}a+ib & c+id \\ -c+id & a-ib\end{array}\right]$, then $A^{-1}$ is equal to

If the matrix $A = \begin{bmatrix} 1 & 2 \\ -5 & 1 \end{bmatrix}$ and $A^{-1} = xA + yI$,where $I$ is a unit matrix of order $2$,then the value of $2x + 3y$ is

Let $a \in R$ and $A$ be a matrix of order $3 \times 3$ such that $\det(A)=-4$ and $A+I=\begin{bmatrix} 1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2 \end{bmatrix}$,where $I$ is the identity matrix of order $3 \times 3$. If $\det((a+1) \operatorname{adj}((a-1) A)) = 2^m 3^n$,where $m, n \in \{0, 1, 2, \ldots, 20\}$,then $m+n$ is equal to:

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

If $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 \\ 3 & 1 \end{bmatrix}$,then $(AB)^{-1} =$