Introduction to group theory/Uniqueness of Inverses


 * Proof

Let $$G$$ be a group and let $$g,a,b \in G$$ such that $$a*g=e=g*a$$ and $$b*g=e=g*b$$. Then substituting we obtain $$a*g=b*g$$. By right cancellation $$a=b$$.
 * Q.E.D.