The inverse of a diagonal non-singular matrix is:

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 $A = \begin{bmatrix} 1 & 2 \\ -1 & 4 \end{bmatrix}$ and $A^{-1} = \alpha I + \beta A$,where $\alpha, \beta \in \mathbb{R}$ and $I$ is the identity matrix of order $2$,then $4(\alpha + \beta) = $

If $A$ is a matrix of order $3$,such that $A(\operatorname{adj} A) = 10I$,then $|\operatorname{adj} A| = $

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

If $A$ and $B$ are non-singular matrices,then which of the following is true?