So I have a group $H$ and a direct product $H \times H$, which is also a group. Then, I am considering a set $A$ = {$(h,h)| h \in H$}. If $A \unlhd G \times G$, I have to show that $H$ is abelian.
My attempt:
So if I consider two arbitrary elements $h_1, h_2 \in H$, then $(h_1,h_1), (h_2,h_2) \in A$. Normality of $A$ means for any $(h,h') \in H \times H$, $(h_1,h_1).(h,h').(h_2,h_2)^{-1} \in A$, and after some steps, I get that $(h_1.h.h_2^{-1}, h_1.h'.h_2^{-1}) \in A$. I am confused as to what the next step is. Can anyone help me?