Answer
See answer below
Work Step by Step
The determinant for the given systems are:
$\det (A)=1.3-(-1).2=5$
$\det (B)=1.4-2.(-2)=8$
Also $AB=\begin{bmatrix}
1 & -1\\
2 & 3
\end{bmatrix}.\begin{bmatrix}
1 &2\\
-2 & 4
\end{bmatrix}=\begin{bmatrix}
3 & -2\\
-4 & 16
\end{bmatrix}$
Hence, $\det (AB)=3.6-(-2)(-4)=40 =\det (A).\det (B)$
Consequently, Theorem 3.2.5, $\det (AB) = 0 = \det (A) .\det(B)$
