Abstract Algebra: Normal Subgroups

Question

Show that, if $N$ is a normal subgroup of $G$, $a \in G$ and $n \in N$, so exist an element $n' \in N$ $|$ $an=n'a$.

Answer 1

$an=ana^{-1}a$, write $n'=ana^{-1}$, $n'\in N$ since $N$ is normal.