SOLUTION: Let g be an element of a group (G, ∗) such that for some one element x ∈ G, x ∗ g = x. Show that g = e.

Algebra ->  sets and operations -> SOLUTION: Let g be an element of a group (G, ∗) such that for some one element x ∈ G, x ∗ g = x. Show that g = e.      Log On


   

Question 1018436: Let g be an element of a group (G, ∗) such that for some one element x ∈ G,
x ∗ g = x. Show that g = e.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Assume otherwise that g is not the identity element e. We have . If we left-multiply both sides by , we obtain , a contradiction.