Answer
See below
Work Step by Step
Given $$\begin{array}{c}{A=\left[\begin{array}{ccc}
{3} & {7} & 1& 2 & 3\\
{1} & {1} & -1 & 0 & 1 \\
4 & 8 & -1 & 6 & 6\\
3 & 7 & 0 & 9 & 4\\
8 & 16 & -1 & 8 & 12 \end{array}\right] }\end{array} $$
So, we get
$$A=\begin{vmatrix} {3} & {7} & 1& 2 & 3\\
{1} & {1} & -1 & 0 & 1 \\
4 & 8 & -1 & 6 & 6\\
3 & 7 & 0 & 9 & 4\\
8 & 16 & -1 & 8 & 12
\end{vmatrix} \rightarrow \begin{vmatrix}
{1} & {1} & -1 & 0 & 1 \\
{3} & {7} & 1& 2 & 3\\
4 & 8 & -1 & 6 & 6\\
3 & 7 & 0 & 9 & 4\\
8 & 16 & -1 & 8 & 12
\end{vmatrix} \rightarrow \begin{vmatrix}
{1} & {1} & -1 & 0 & 1 \\
{0} & {4} & 4& 2 & 0\\
0 & 4 & 3 & 6 & 2\\
0& 4 & 3 & 9 & 1\\
0 & 8 & 7 & 8 & 4
\end{vmatrix} \rightarrow \begin{vmatrix}
{1} & {1} & -1 & 0 & 1 \\
{0} & {1} & 1& \frac{1}{2} & 0\\
0 & 4 & 3 & 6 & 2\\
0& 4 & 3 & 9 & 1\\
0 & 8 & 7 & 8 & 4
\end{vmatrix} \rightarrow \begin{vmatrix}
{1} & {1} & -1 & 0 & 1 \\
{0} & {1} & 1& \frac{1}{2} & 0\\
0 &0 & -1 & 4 & 2\\
0& 0 & -1 & 4 & 1\\
0 & 0 & -1 & 4 & 4
\end{vmatrix} \rightarrow \begin{vmatrix}
{1} & {1} & -1 & 0 & 1 \\
{0} & {1} & 1& \frac{1}{2} & 0\\
0 &0 & -1 & 4 & 2\\
0& 0 & 0 & 3 & -1\\
0 & 0 & 0& 0 &2
\end{vmatrix}$$
\begin{array}{l}{\text { Determinant of triangular matrix is the product of its diagonal elements, so: }} \\ {\text {det }A=-4 \cdot 1 \cdot 1 \cdot (-1) \cdot 3 \cdot 2=24}\end{array}
