If $A = \begin{bmatrix} 1 & 2 & 0 \\ 0 & 1 & 2 \\ 2 & 0 & 1 \end{bmatrix}$,then find $adj(A)$.

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 $(\operatorname{adj} A)^{-1}+\operatorname{adj} A^{-1}=$

If $P = \begin{vmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{vmatrix}$ is the adjoint of a $3 \times 3$ matrix $A$ and $\det(A) = 4$,then $\alpha$ is equal to

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 $A^{-1}=$

$A=\left[\begin{array}{rr}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]$ and $AB=BA=I$,then $B$ is equal to

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