This question already has an answer here:
Let $G$ be a finitely generated group. Show that if Aut($G$) is the trivial group, then so is $G$.
I know that if Aut($G$) is the trivial group then $G$ must be abelian but I'm not sure how to use that fact here. What's a good way to show that $G$ is the trivial group, given that Aut($G$) is also trivial?
Note: This question is different from |G|>2 implies G has non trivial automorphism because there is no proof provided in that question that the opposite is also true, i.e. that $|G| \leq 2 \Rightarrow$ Aut($G$) is trivial.