If $A = \begin{bmatrix} 1 & a & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7 \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} 13 & 2 & -7 \\ -3 & b & 2 \\ -2 & 0 & 1 \end{bmatrix}$,then the values of $a$ and $b$ are respectively

If $A=\left[\begin{array}{ll}2 & -2 \\ 2 & -3\end{array}\right]$ and $B=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]$,then $(B^{-1} A^{-1})^{-1} = ?$

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:

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 $A$ and $B$ are invertible matrices of the same order, then which of the following is not correct?

Let $A$ be a square matrix of order $3$. Choose the correct option regarding the following statements:
$I$. There exists a matrix $B$ of order $3$ such that $AB = I_3$
$II$. There exists a matrix $C$ of order $3$ such that $CA = I_3$
$III$. $A$ is invertible