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

Let $\alpha, \beta, \gamma$ be real numbers. If $A=\begin{bmatrix} 7 & 3 & \alpha \\ \beta & 1 & -11 \\ -5 & \gamma & 19 \end{bmatrix}$ is a $3 \times 3$ matrix satisfying $A\begin{bmatrix} 5 \\ -13 \\ 11 \end{bmatrix}=\begin{bmatrix} -290 \\ -119 \\ 210 \end{bmatrix}$, then $(\operatorname{adj} A)^{-1}+\operatorname{adj} A^{-1}=$

Let $F(\alpha ) = \begin{bmatrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{bmatrix}$,where $\alpha \in \mathbb{R}$. Then $[F(\alpha )]^{-1}$ is equal to

Find the inverse of the matrix,if it exists: $\left[\begin{array}{ccc}1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0\end{array}\right]$

$A$ is an involutory matrix given by $A = \begin{bmatrix} 0 & 1 & -1 \\ 4 & -3 & 4 \\ 3 & -3 & 4 \end{bmatrix}$. Then the inverse of $\frac{A}{2}$ will be:

If $P$ is a $3 \times 3$ real matrix such that $P^{T} = aP + (a - 1)I$,where $a > 1$,then $..........$