document.write( "Question 1018436: Let g be an element of a group (G, ∗) such that for some one element x ∈ G,
\n" ); document.write( "x ∗ g = x. Show that g = e. \n" ); document.write( "

Algebra.Com's Answer #634538 by richard1234(7193) $\"\"$ $\"About$

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Assume otherwise that g is not the identity element e. We have

. If we left-multiply both sides by

, we obtain

, a contradiction. \n" ); document.write( "

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