Solution
= Solution
The two-by-two <matrix inverse> formula gives
$$
M^{-1}=\begin{pmatrix}-4&3\\3&-2\end{pmatrix},\quad N^{-1}=\begin{pmatrix}4&-3\\-1&1\end{pmatrix},\quad(MN)^{-1}=\begin{pmatrix}-25&18\\7&-5\end{pmatrix}.
$$
Multiplication in the reversed order gives
$$
\boxed{N^{-1}M^{-1}=\begin{pmatrix}-25&18\\7&-5\end{pmatrix}=(MN)^{-1}.}
$$
The order reversal is needed because applying the inverse undoes the original two <linear maps> in reverse sequence.