Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2003 / Paper 1 / 5 / b / iii

Use $A=M$ and $B=N$ from part (a). The proposed unreversed product iswhich differs from the actual inverse $\left(\begin{array}{cc}-25& 18\\ 7& -5\end{array}\right)$. Both original matrices are invertible matrices, so this is a valid counterexample. The universally valid order is $\boxed{(AB{)}^{-1}=B^{-1}{A}^{-1}}$.