If $A = \begin{bmatrix} 1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4 \end{bmatrix}$ and $A(\operatorname{adj} A) = kI$,then the value of $(k+1)^4$ is

If $F(\alpha ) = \begin{bmatrix} \cos \alpha & - \sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{bmatrix}$ and $G(\beta ) = \begin{bmatrix} \cos \beta & 0 & \sin \beta \\ 0 & 1 & 0 \\ - \sin \beta & 0 & \cos \beta \end{bmatrix}$,then $[F(\alpha ) G(\beta )]^{-1} = $

If $A=\begin{bmatrix} 1 & 0 & -2 \\ -2 & -1 & 2 \\ 3 & 4 & 1 \end{bmatrix}$,then $A^{-1}=$

Consider the following statements:
Statement $I$: If $A$ is a non-singular matrix, then $A^{-1}$ exists.
Statement $II$: If $A$ and $B$ are symmetric matrices of the same order, then $(AB - BA)$ is a skew-symmetric matrix.
Choose the correct option.

If $A$ and $B$ are non-singular matrices of the same order,then $\text{Adj}(AB)$ is:

If the matrix $A=\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}$ satisfies the matrix equation $A^2-4A-5I=0$, then $A^{-1}=$