1. The problem statement, all variables and given/known data suppose that G is a group in which every non-identity element has order two. Show that G is commutative. 2. Relevant equations 3. The attempt at a solution Is my answer correct? Suppose that a,b and ab all have order two. we will show that a and b commute. By assumption, e=(ab)^2 =abab As a and b are their own inverses, multiplying on the left by a and then b, we get ba=ab.