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.

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.

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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) (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.
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