If the determinant of the adjoint of a (real) matrix of order $3$ is $25$,then the determinant of the inverse of the matrix is

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 1 \\ 1 & 2 & 1 \end{bmatrix}$,then $|\operatorname{Adj}(A^2)| = $

If the adjoint of a $3 \times 3$ matrix $P$ is $\begin{bmatrix} 1 & 4 & 4 \\ 2 & 1 & 7 \\ 1 & 1 & 3 \end{bmatrix}$,then the possible value$(s)$ of the determinant of $P$ is (are):

If $A = \begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4 \end{bmatrix}$,then verify that $A \text{ adj } A = |A| I$. Also,find $A^{-1}$.

If $A = \begin{bmatrix} 0 & 1 & -1 \\ 2 & 1 & 3 \\ 3 & 2 & 1 \end{bmatrix}$,then evaluate $(A \cdot (\text{adj } A) \cdot A^{-1}) A$.

Let $A$ be a $3 \times 3$ real matrix. If $\det(2 \operatorname{Adj}(2 \operatorname{Adj}(\operatorname{Adj}(2 A))))=2^{41}$,then the value of $\det(A^{2})$ is equal to ..... .