If $G$ is a cyclic group where both $a$ and $b$ are generators. How would I prove that $f:G \rightarrow G$ given by $f(a^i)=b^i$ is an automorphism.
I know that an automorphism is the identity map. So if $G$ is cyclic of order $n$. So I believe I have to show that $f$ is a well defined homomorphism, but I'm not exactly sure how to do this.