If $A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1 \end{bmatrix}$,then the value of the determinant of $A^{-1}$ is

If $A$ and $B$ are non-singular square matrices of the same order,then $adj(AB)$ is equal to:

If $A = \begin{bmatrix} k & 2 \\ -2 & -k \end{bmatrix}$,then $A^{-1}$ does not exist if $k =$

If $A$ is a square matrix of order $3$ such that $\operatorname{det}(A)=3$ and $\operatorname{det}\left(\operatorname{adj}\left(-4 \operatorname{adj}\left(-3 \operatorname{adj}\left(3 \operatorname{adj}\left((2A)^{-1}\right)\right)\right)\right)\right)=2^{m} 3^{n}$,then $m+2n$ is equal to:

If $A = \begin{bmatrix} 1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4 \end{bmatrix}$,then $(A^2 - 5A)A^{-1} = $

If $A = \begin{bmatrix} 1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4 \end{bmatrix}$,then $A(\operatorname{adj} A) = $