Suppose $\displaystyle F$ is a finite field of characteristic 3 and $\displaystyle \phi : F \rightarrow F$ is the map defined by $\displaystyle \phi(a)=a^3$. Prove that $\displaystyle \phi$ is surjective.

How do I do this? I know how to prove that it is an injective ring homomorphism. But I don't know how to prove it is surjective. Thanks.