Matrices $A$ and $B$ will be inverse of each other only if

If $A = \frac{1}{7} \begin{bmatrix} 3 & -2 & 6 \\ -6 & -3 & 2 \\ -2 & 6 & 3 \end{bmatrix}$,then:

If $A = \begin{bmatrix} 1 & \tan x \\ -\tan x & 1 \end{bmatrix}$,then $A^T \cdot A^{-1} = $

Suppose $n > 1$ and $A$ is a non-singular matrix of order $n$ such that $|\operatorname{adj} A| = |\operatorname{adj}(\operatorname{adj} A)|$. Then the matrix whose rank is $n$ is:

Let $A$ be an invertible square matrix of order $3 \times 3$. Then $|(\text{adj} A) \cdot A|$ is

If $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 3 \\ 1 & 0 & 1 \end{bmatrix}$,then $|\operatorname{adj} A| = $ . . . . . . .