The inverse of the matrix $A = \begin{bmatrix} 2 & -1 & 4 \\ 4 & -3 & 1 \\ 1 & 2 & 1 \end{bmatrix}$ is $B = \frac{1}{37} \begin{bmatrix} -5 & 9 & 11 \\ -3 & -2 & 14 \\ 11 & -5 & k \end{bmatrix}$, then the value of $k$ is...

For any $2 \times 2$ matrix $A$,if $A(\text{adj } A) = \begin{bmatrix} 10 & 0 \\ 0 & 10 \end{bmatrix}$,then $|A|$ is equal to:

${\left[ {\begin{array}{*{20}{c}}1&3\\3&{10}\end{array}} \right]^{ - 1}} = $

Which of the following matrices is invertible?
$A_{1}=\begin{bmatrix} 4 & 2 \\ 2 & 1 \end{bmatrix}$
$A_{2}=\begin{bmatrix} -1 & -2 & 3 \\ 4 & 5 & 7 \\ 2 & 4 & -6 \end{bmatrix}$
$A_{3}=\begin{bmatrix} 1 & 0 & 0 \\ 5 & 2 & 1 \\ 7 & 2 & 1 \end{bmatrix}$
$A_{4}=\begin{bmatrix} 1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1 \end{bmatrix}$

The element of the second row and third column in the inverse of $\begin{bmatrix} 1 & 2 & 1 \\ 2 & 1 & 0 \\ -1 & 0 & 1 \end{bmatrix}$ is

If $A$ is a square matrix of order $3$ and $|A| = 8$,then $|adj(A)| = $