Definition:Bijection/Definition 3

Definition
A mapping $f: S \to T$ is a bijection iff:
 * the inverse $f^{-1}$ of $f$ is a mapping from $T$ to $S$.

That is, iff $f$ admits an inverse.

Also see

 * Equivalence of Definitions of Bijection


 * Inverse of Bijection is Bijection, where it is shown that this inverse mapping is also a bijection.