# 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.