Answer
$\det (A)=-153$
Work Step by Step
We have the cofactor expansion theorem is:
$\det (A)=a_{21}C_{21}+a_{22}C_{22}+a_{23}C_{23}$
with $C_{ij}=(-1)^{i+j}.M_{ij}$
to evaluate the given determinant of row 2:
$\det (A)=(-7)C_{21}+1C_{22}+(-3)C_{23}$
$\det (A)=(-7)\begin{vmatrix}
1 & -4 \\
5 & -2
\end{vmatrix}+1\begin{vmatrix}
2 & -4 \\
1 & -2
\end{vmatrix}+(-3)\begin{vmatrix}
2 & 1 \\
1 & 5
\end{vmatrix}$
Plug in the given values:
$\det (A)=(-7).18+1.0+(-3).9$
$\det (A)=-126+0-27$
$\det (A)=-153$
