Diagonalizable vector-space-endomorphisms.

Question

I'm new here and need help with a problem:

Let $A$ be in $Mat(n,K)$ and $f_A:K^n \rightarrow K^n, f_A(x)=Ax.$

I have to show, that $A$ is similar to a diagonal Matrix $D$ $\iff$ $f_A$ is diagonalisable.

Thanks. feelsbadman