If $A$ is a square matrix of order $3$ and $|A|=5$,then $|A \text{ adj. } A|$ is

If $A$ and $B$ are non-singular matrices of order $2$ such that $(AB)^{-1} = \frac{1}{6} \begin{bmatrix} -7 & -3 \\ 2 & 3 \end{bmatrix}$ and $A^{-1} = \frac{1}{3} \begin{bmatrix} 4 & 3 \\ -1 & 0 \end{bmatrix}$,then $B^{-1} = $

If $A = \begin{bmatrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 3 \end{bmatrix}$ and $B = \operatorname{adj} A$,$C = 5A$,then $\frac{|\operatorname{adj} B|}{|C|} = $

If $A = \begin{bmatrix} 1 & -\tan(\theta/2) \\ \tan(\theta/2) & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & \tan(\theta/2) \\ -\tan(\theta/2) & 1 \end{bmatrix}$ then $A^{-1}B$ is equal to

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$, $C = \begin{bmatrix} 7 & 3 \\ 0 & 6 \end{bmatrix}$ and $AB = C$, then the inverse of matrix $B$ is

If $A = \begin{bmatrix} 1 & 2 \\ -4 & -1 \end{bmatrix}$, then $A^{-1}$ is