If $A$ is a square matrix of order $3 \times 3$,then $|\operatorname{adj} A| =$ . . . . . . .

If $A$ is a singular matrix,then $\text{adj } A$ is

$\begin{aligned} & A(\alpha, \beta)=\left[\begin{array}{ccc}\cos \alpha & \sin \alpha & 0 \\ -\sin \alpha & \cos \alpha & 0 \\ 0 & 0 & e^\beta\end{array}\right] \\ & \Rightarrow[A(\alpha, \beta)]^{-1}=\end{aligned}$

If $A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & a & 3 \\ 3 & 2 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -2 & 0 & b \\ 7 & -1 & -2 \\ c & 1 & 1 \end{bmatrix}$ and if matrix $B$ is the inverse of matrix $A$,then the value of $4a + 2b - c$ is:

If $A=\begin{bmatrix} 2 & -3 \\ 5 & -7 \end{bmatrix}$,then $A-A^{-1}=$

If $A$ is an invertible matrix of order $n$,then the determinant of $\operatorname{adj} A$ is equal to :