I'm having a hard time with this problem, could someone point me in the right direction?

How can I show the following is false?

For all sets $\displaystyle A$ and $\displaystyle B$, and all functions $\displaystyle f : A \rightarrow B$, $\displaystyle g : B \rightarrow A$, if $\displaystyle g \circ f = I_{A}$, then $\displaystyle f \circ g = I_{B}$.

Obviously, I need to find a counterexample, but I'm having a hard time coming up with one.