If $A$ is a non-singular matrix,then $A(\text{adj } A) =$

If $P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a $3 \times 3$ matrix $A$ and $|A| = 4$,then the value of $\alpha$ is:

If $A$ and $B$ are non-singular matrices,then which of the following is true?

Find $P^{-1},$ if it exists,given $P=\left[\begin{array}{cc}10 & -2 \\ -5 & 1\end{array}\right].$

If $A$ is a $3 \times 3$ non-singular matrix such that $AA' = A'A$ and $B = A^{-1}A'$,then $BB'$ equals:

The inverse of the matrix $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}$ is