If $A$ is a $3 \times 3$ matrix such that $|5 \times \text{adj} A|=5$,then $|A|$ 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 $A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right]$,then $A^{-1}=$

The inverse of a matrix $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is

If $A = \begin{bmatrix} 2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3 \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} 3 & -1 & 1 \\ \alpha & 6 & -5 \\ \beta & -2 & 2 \end{bmatrix}$,then the values of $\alpha$ and $\beta$ are respectively:

If $B = \begin{bmatrix} 1 & \alpha & 2 \\ 1 & 2 & 2 \\ 2 & 3 & 3 \end{bmatrix}$ is the adjoint of a $3 \times 3$ matrix $A$ and $|A| = 5$,then $\alpha$ is equal to