What elements of $G$ are in the equivalence class containg $a$, for an equivalence relation $\sim$?

Question

For question (b), it seems to me that there are only two elements in the equivalence class of $a$ in $G$, which is $a$ and $a^{-1}$. Am I wrong?

Thanks a lot in advance!!

Answer 1

Hint: If $|a|\gt2$, then $|\bar a|=2$. Otherwise, it's $|\bar a|=1$.