If $A=\begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & x & 1 \end{bmatrix}$ and $A^{-1}=\frac{1}{2}\begin{bmatrix} 1 & -1 & 1 \\ -8 & 6 & 2y \\ 5 & -3 & 1 \end{bmatrix}$, then the point $(x, y)$ lies on the curve represented by the equation:

If $A=\left[\begin{array}{ccc}1 & 2 & 1 \\ -1 & 1 & 3\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & 2 \\ -3 & 1 \\ 0 & 2\end{array}\right]$,then find $(AB)^{-1}$.

Let $A = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}$ and $B = I + \operatorname{adj}(A) + (\operatorname{adj} A)^2 + \dots + (\operatorname{adj} A)^{10}$. Then,the sum of all the elements of the matrix $B$ is:

If $A$ is a square matrix of order $3 \times 3$,then $|\operatorname{adj} A| =$ . . . . . . .

If $A = \begin{bmatrix} 3 & 4 \\ 5 & 7 \end{bmatrix}$,then $A(adj A) = $

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: