Here is the question:
Let $A,B \in \frak gl$$(V)$, where $V$ is a finite-dimensional vector space over the field $\mathbb{F} = \mathbb{R}$ or $\mathbb{C}$, and show that the following statements are equivalent:
(a) $[A,B] = 0$.
(b) $\exp(sA)$ and $\exp(tB)$ commute for all $s,t \in \mathbb{F}$.
(c) $\exp(sA +tB) = \exp(sA)\exp(tB)$ for all $s,t \in \mathbb{F}$.
(a) $\Rightarrow$ (b) follows by commutativity of the flows, but the rest is unclear. Expanding the power series out doesn't seem to help. For small enough $s$ and $t$ we can apply $\log$, but I'm not sure if this helps either.
I'm really clueless right now. I would appreciate any help. Thanks.