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

If $A = [a_{ij}]_{3 \times 3}$, where $a_{ij} = \begin{cases} 1, \text{ if } i + j \text{ is even} \\ 0, \text{ if } i + j \text{ is odd} \end{cases}$, then $adj(A) = \dots$

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

If $A = \begin{bmatrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{bmatrix}_{3 \times 3}$,then $A^{-1} = $

If $|A| = -3$ and $A^{-1} = \begin{bmatrix} 1 & 0 & 0 \\ -1 & \frac{1}{3} & 0 \\ 3 & \frac{2}{3} & -1 \end{bmatrix}$,then $(\operatorname{adj} A)$ is

Find the inverse of the matrix $A = \left[\begin{array}{ll}4 & 5 \\ 3 & 4\end{array}\right]$,if it exists.