Let $G$ be a group and $g\in G$. Prove or Disprove: If $o(g^2)=2$ then $o(g)=4$.

Question

Let $G$ be a group and $g\in G$.

Prove or Disprove: If $o(g^2)=2$ then $o(g)=4$.

I tried to disprove it but without success, if it's a proof how can we prove it?

Answer 1

Observe that $g^4 = e$ so order of $g$ can only be $1,2,4$ now finish