If $A$ is a non-singular matrix such that $(A-2I)(A-3I)=O$, then $\frac{1}{5}A + \frac{6}{5}A^{-1} = $

If $A = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix}$, then which of the following is true?

If $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix}$, then $\operatorname{adj}(\operatorname{adj} A)$ is equal to

If $A$ is a $2 \times 2$ order non-singular matrix,then the determinant of $A^{-1}$ is . . . . . . .

If $\begin{bmatrix} 5 & a & -7 \\ b & -7 & c \\ -7 & d & -1 \end{bmatrix}$ is the adjoint of the matrix $\begin{bmatrix} 1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2 \end{bmatrix}$,then $a+b+c+d=$

If $A$ is a $3 \times 3$ matrix and $|A|=2$,then $|3 \operatorname{adj}(|3A|A^2)|$ is equal to $.........$.