If ${I_3}$ is the identity matrix of order $3$,then ${I_3}^{-1}$ is

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

For two invertible matrices $A$ and $B$ of suitable orders,the value of $(AB)^{-1}$ is

If $A = \begin{bmatrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0 \end{bmatrix}$, $B = \operatorname{adj} A$ and $C = 5A$, then find the value of $\frac{|\operatorname{adj} B|}{|A|^4}$.

If $P(\theta) = \begin{bmatrix} 1 & \cot \theta \\ -\cot \theta & 1 \end{bmatrix}$ and $PQ = I$,then find $(\csc^2 \theta)Q$,where $I$ is an identity matrix of order $2 \times 2$.

If $A$ is a square matrix satisfying the equation $A^2 - 5A + 7I = 0$,where $I$ is the identity matrix and $0$ is the null matrix of the same order,then $A^{-1} = $