If $A = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 1 & 6 \end{bmatrix}$ and $|\text{adj}(\text{adj } A)|(\text{adj } A)^{-1} = kA$,then $k = $

The inverse of the matrix $\left[\begin{array}{ccc}7 & -3 & -3 \\ -1 & 1 & 0 \\ -1 & 0 & 1\end{array}\right]$ is

If $A=\begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix}$ and $B=\begin{bmatrix} 4 & 1 \\ 3 & 1 \end{bmatrix}$,then $(A+B)^{-1} = $

If $A$ is a matrix of order $3$ whose determinant is equal to $6$,then $\operatorname{det}(\operatorname{adj} A) = $

If matrix $A = \begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix}$ and $A^{-1} = \alpha I + \beta A$ where $I$ is a unit matrix of order $2$ and $\alpha, \beta$ are constants,then the value of $\alpha + \beta + \alpha \beta$ is

If $A$ is a square matrix of order $3$,then consider the following statements.
$I$. If $|A|=0$,then $|\operatorname{Adj} A|=0$
$II$. If $|A| \neq 0$,then $|A^{-1}|=|A|^{-1}$
Which of the above statements is/are true?