Answer
$\det (A)=-171$
Work Step by Step
We have the cofactor expansion theorem for the 1st row:
$\det (A)=a_{12}C_{12}+a_{22}C_{22}+a_{32}C_{32}+a_{42}C_{42}$
with $C_{ij}=(-1)^{i+j}.M_{ij}$
So, we get:
$\det (A)=2C_{12}+1C_{22}+0C_{32}+1C_{42}$
$\det (A)=1\begin{vmatrix}
1 & -1 & -6 \\
3 & 2 & 3 \\
0 & -5 & 2
\end{vmatrix}+2\begin{vmatrix}
-4 & -3 & -2 \\
3 & 2 & 3 \\
0 & -5 & 2
\end{vmatrix}+0\begin{vmatrix}
-4 & -3 & -2 \\
1 & -1 & -6 \\
0 & -5 & 2
\end{vmatrix}+0\begin{vmatrix}
-4 & -3 & -2 \\
1 & -1 & -6 \\
0 & -5 & 2
\end{vmatrix}$
Plug in the given values:
$\det (A)=1.(-1)[1.(4+15)-3.(-2-30)]+2[-4(4+15)-3(-6-10)]+0+0$
$\det (A)=-115-56$
$\det (A)=-171$
