If $\displaystyle A$ and $\displaystyle B$ are $\displaystyle n$ by $\displaystyle n$ matrices. If

$\displaystyle AB = BA$ then $\displaystyle e^{A+B} = e^A \cdot e^B$.

However,

$\displaystyle e^{A+B} = e^A \cdot e^B$ does not imply that $\displaystyle AB = BA$.

I'm looking for a counter example illustrating this