If $B = \begin{bmatrix} 3 & \alpha & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3 \end{bmatrix}$ is the adjoint of a $3 \times 3$ matrix $A$ and $|A| = 4$,then $\alpha$ is equal to:

If $A, B$ and $(\operatorname{adj}(A^{-1})+\operatorname{adj}(B^{-1}))$ are non-singular matrices of the same order,then the inverse of $A(\operatorname{adj}(A^{-1})+\operatorname{adj}(B^{-1}))^{-1}B$ is equal to

If possible,using elementary row transformations,find the inverse of the following matrix:
$\left[\begin{array}{ccc}2 & -1 & 3 \\ -5 & 3 & 1 \\ -3 & 2 & 3\end{array}\right]$

The inverse of $\begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \end{bmatrix}$ is

Let $A$ be a matrix of order $3 \times 3$ and $\det(A) = 2$. Then $\det(\det(A) \cdot \operatorname{adj}(5 \operatorname{adj}(A^3)))$ is equal to:

If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$, then $\operatorname{Adj}(\operatorname{Adj}(\operatorname{Adj} A)) = $