Let $G$ be a group, $N \triangleleft G$ and $\bar{G} = G/N$. Prove that for every two elements $\bar{a},\bar{b} \in \bar{G}$, the following is true: $\bar{a}\bar{b} = \bar{b}\bar{a}$ if and only if $a^{-1}b^{-1}ab \in N$.

I am having trouble with quotient groups and the textbook does not help me simplify. I am struggling to see the connection.