Prove that H is a normal subgroup if and only if, $\forall a , b \in G, ab \in$ H implies $ba\in H.$

Question

Let H be a subgroup of G. Prove that H is a normal subgroup if and only if, $\forall a , b \in G, ab \in$ H implies $ba \in H.$

I don't have a problem to prove one of the implications, however, this one which I have to prove that H is normal is a bit problematic... I want a hint on how to start

Answer 1

Hint: suppose $h\in H$ and $a\in G$, and set $b:=a^{-1}h$.