If $A$ is a $3 \times 3$ non-singular matrix and if $|A|=3$,then $|(2A)^{-1}|$ is

If $A$ is a square matrix of order $3$, then $|\operatorname{Adj}(\operatorname{Adj} A^2)|=$

If $A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix}$ and $A^{-1} = \frac{1}{2} \begin{bmatrix} 1 & -1 & 1 \\ -8 & 6 & 2c \\ 5 & -3 & 1 \end{bmatrix}$,then the values of $a$ and $c$ are respectively:

If $A = \begin{bmatrix} \cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$,then $\operatorname{adj} A = $

If $A = \begin{bmatrix} 5 & 2 \\ 3 & 1 \end{bmatrix}$,then $A^{-1} = $

If $A$ is a non-zero square matrix of order $n$ with $\det(I+A) \neq 0$ and $A^3=O$, where $I$ and $O$ are the identity and null matrices of order $n \times n$ respectively, then $(I+A)^{-1}$ is equal to