I don't know how to prove the following : Let $\displaystyle f:A \to B$ be a function. Prove that $\displaystyle f$ has an inverse if and only if $\displaystyle f$ is bijective.

I'm lacking of any idea about proving $\displaystyle \Rightarrow$ and $\displaystyle \Leftarrow$.

I'm asking for a little push in the right direction and not the full answer. Thanks a lot.

P.S.: I got assigned to do this in a vector calculus class, if it helps.