If $A$ is a matrix of order $3$ whose determinant is equal to $6$,then $\operatorname{det}(\operatorname{adj} A) = $

Let $A$ be a square matrix of order $3$ such that $\operatorname{det}(A)=-2$ and $\operatorname{det}(3 \operatorname{adj}(-6 \operatorname{adj}(3 A)))=2^{m+n} \cdot 3^{mn}$,where $m > n$. Then $4m+2n$ is equal to . . . . . .

Given $A$ and $C$ are involutory matrices and $B$ is a non-singular matrix,then $(AB^{-1}C)^{-1}$ is equal to -

If $A$ is a square matrix of order $4$ and $B = \text{Adj}(A)$,where $|B| = 27$,then the value of $|A^{-1} \text{Adj}(3AB)|$ is,(where $A^{-1}$ denotes the inverse of matrix $A$ and $\text{Adj}(A)$ denotes the adjoint of matrix $A$):

The inverse of matrix $A = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ is

If $A=\begin{bmatrix} 1 & 2 & 2 \\ 3 & 2 & 3 \\ 1 & 1 & 2 \end{bmatrix}$ and $A^{-1}=\begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix}$, then $\sum_{1 \leq i, j \leq 3} a_{ij} =$