Totally invariant subvarieties of ${\mathbf{P}}^n$

Let $f:{\mathbf{P}}_{\mathbb{C}}^n\to {\mathbf{P}}_{\mathbb{C}}^n$ be an endomorphism of degree greater than one. We prove that every irreducible Zariski closed subset $V$ with $f^{-1}(V)=V$ is a linear subspace.