If $A = \begin{bmatrix} 2 & 1 & 0 \\ 0 & 2 & 1 \\ 1 & 0 & 2 \end{bmatrix}$,then $|\operatorname{adj} A|$ is equal to

The values of $t$ such that the matrix $\begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 & t \\ 4 & 7 - t & -6 \end{bmatrix}$ has no inverse,are

If $\begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} A \begin{bmatrix} -3 & 2 \\ 5 & -3 \end{bmatrix} = I_2$,then $A =$

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:

If $A$ is a matrix of order $3 \times 3$,then $(A^2)^{-1}$ is equal to

If $A$ is a $3 \times 3$ matrix such that $|5 \times \text{adj} A|=5$,then $|A|$ is equal to