If every element of a square non-singular matrix $A$ of order $n$ is multiplied by $k$ and the new matrix is denoted by $B$,then how are $|A^{-1}|$ and $|B^{-1}|$ related?

Let $A$ be a $3 \times 3$ matrix such that $A+A^{T}=O$. If $A\begin{bmatrix}1\\ -1\\ 0\end{bmatrix}=\begin{bmatrix}3\\ 3\\ 2\end{bmatrix}$, $A^{2}\begin{bmatrix}1\\ -1\\ 0\end{bmatrix}=\begin{bmatrix}-3\\ 19\\ -24\end{bmatrix}$ and $\det(\text{adj}(2\text{adj}(A+I))) = (2)^\alpha \cdot(3)^\beta \cdot(11)^\gamma$, then $\alpha+\beta+\gamma$ is equal to . . . . . . .

Let $A$ be a $2 \times 2$ matrix.
$Statement-1: adj(adj A) = A$
$Statement-2: |adj A| = |A|$

Let $A$ be a $n \times n$ matrix such that $A$ is an upper-triangular matrix. Then $adj(A) =$

If $\operatorname{adj}\begin{bmatrix} 1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1 \end{bmatrix} = \begin{bmatrix} 5 & a & -2 \\ 1 & 1 & 0 \\ -2 & -2 & b \end{bmatrix}$, then $[a \quad b]$ is equal to

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