1. The problem statement, all variables and given/known data show that a group G is abelian if g^2 = 1 for all g in G. Give an example showing that converse is false. 3. The attempt at a solution Suppose g^2 = 1. gg = 1, (g^-1)gg = g^-1 g = g^-1 -- means self inverse. but I'm not sure how to show G is abelian.. and I don't know how I find counterexample.