A condition under which a group must be abelian (2)

#group_theory

Let $G$ be a group, and $G \times G$ the direct product. The set $D = {(g, g,) ∣ g \in G}$ is a subgroup of $G \times G$ . Prove that if $D$ is normal in $G \times G$ then $G$ is abelian.

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Let $G$ be a group, and $G\times G$ the direct product. The set $D=\{(g,g,)\mid g\in G\}$ is a subgroup of $G\times G$. Prove that if $D$ is normal in $G\times G$ then $G$ is abelian.