Solution
= Solution
Direct <matrix multiplication> gives $MN=\begin{pmatrix}5&18\\7&25\end{pmatrix}$. The three <determinants> are $\det M=8-9=-1$, $\det N=4-3=1$, and $\det(MN)=125-126=-1$. Hence $\boxed{\det(MN)=(-1)(1)=\det M\det N}$, as required.