For any $2 \times 2$ matrix $A$,if $A(\text{adj } A) = \begin{bmatrix} 10 & 0 \\ 0 & 10 \end{bmatrix}$,then $|A| = $

Matrices $A$ and $B$ will be inverse of each other only if

The inverse of $\begin{bmatrix} 2 & -3 \\ -4 & 2 \end{bmatrix}$ is

Let $A$ be a nonsingular square matrix of order $3 \times 3$. Then $|adj\, A|$ is equal to

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 . . . . . .

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: