Let $A = \begin{bmatrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{bmatrix}$. If $B = \text{adj } A$, then the matrix $B^{-1}$ 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 $(\operatorname{adj} A)^{-1}+\operatorname{adj} A^{-1}=$

Suppose $n > 1$ and $A$ is a non-singular matrix of order $n$ such that $|\operatorname{adj} A| = |\operatorname{adj}(\operatorname{adj} A)|$. Then the matrix whose rank is $n$ is:

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

Find the inverse of the matrix (if it exists): $\left[\begin{array}{ccc}1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4\end{array}\right]$

The adjoint of the matrix $A = \begin{bmatrix} 2 & -3 \\ 3 & 5 \end{bmatrix}$ is