Let $A$ be a non-singular matrix of order $n$ and $|A|=k$, then $(\operatorname{adj} A)^{-1}$ is

If $A=\begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ and $A^{2}-5A-6I=0$,then $A^{-1}=$

If $A^{-1}=\frac{-1}{2}\left[\begin{array}{cc}5 & 8 \\ -1 & 2\end{array}\right]$,then $2A+I_2=$,where $I_2$ is a unit matrix of order $2$.

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

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

If $A = \begin{bmatrix} 2 & 1 & 3 \\ -1 & 2 & 0 \\ 4 & 1 & 3 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & 2 & 1 \\ 1 & 2 & 3 \\ 3 & 1 & 0 \end{bmatrix}$,then $\operatorname{det}(2 B^{-1} A^{-1})$ is equal to