**Solution:** Let a, b∈G such that a ≠ e, b ≠ e.

*Then according to the question,*

a^{2} = e, b^{2} = e.

Also ab∈G and So (ab)^{2} = e

Now (ab)^{2} = e

⟹ (ab) (ab) = e

⟹ a(ab ab) b = a e b

⟹ a^{2}bab^{2} = ab

⟹ e ba e = ab

⟹ ba = ab .

Hence G is abelian. **(Proved)**