Answer
See below
Work Step by Step
Given $$ A=\begin{bmatrix}
1 & 2 & 3 & 0 & 0\\
2 & -1 & 4 & 0 & 0\\
6 & 1 & 1 & 0 & 0\\
0 & 0 & 0 & 4 & 3\\
0 & 0 & 0 & -1 & -2
\end{bmatrix}$$
So, we get
$det (A)=\begin{vmatrix}
1 & 2 & 3 & 0 & 0\\
2 & -1 & 4 & 0 & 0\\
6 & 1 & 1 & 0 & 0\\
0 & 0 & 0 & 4 & 3\\
0 & 0 & 0 & -1 & -2
\end{vmatrix}\\
=\begin{vmatrix}
1 & 2 & 3 \\ 2 & -1 & 4 \\ 6 & 1 & 1
\end{vmatrix}.\begin{vmatrix}
4 & 3 \\ -1 & -2
\end{vmatrix}\\
=(1.(-1).1+2.4.6+3.2.1-1.4.1-2.2.1-3.(-1).6).(4.(-2)-3.(-1))\\
=(-1+48+6-4-4+18).(-8+3)\\
=43.(-5)\\
=-315$
