Answer
$det A\cdot det B=det (AB)$
Work Step by Step
Calculate $AB$:
$$\begin{align*}
AB&=\begin{bmatrix}2&-1\\1&2\end{bmatrix}\begin{bmatrix}3&5\\-2&-4\end{bmatrix}\\
&=\begin{bmatrix}8&14\\-1&-3\end{bmatrix}.
\end{align*}$$
Calculate $det A$, $det B$ and $det (AB)$:
$$\begin{align*}
det A&=2\cdot 2-1\cdot(-1)=5.\\
det B&=3\cdot (-4)-5\cdot(-2)=-2.\\
det (AB)&=8\cdot (-3)-14\cdot(-1)=-10.
\end{align*}$$
We notice that $det A\cdot det B=det (AB)$.
