If a^(- 1) = a for every a in G then G is abelian.

Modern Algebra
Group Theory (XX)
Relation between Cyclic Group and Abelian Group

Show that if every element of the group G is its own inverse, then G is abelian.

Solution Summary

It is shown that if every element of the group G is its own inverse, then G is abelian. The solution is detailed and well presented.