People who know mathematics, can u answer this questoin please.?

Question

If * is a binary operation on a set S, an element x of S is an idempotent for * if x*x=x. Prove that a group h

Answer 1

I guess that the missing part of the question is "has exactly one idempotent".

One way to prove this is to show that any idempotent x of a group has to equal the identity element e (and note that e is always an idempotent).

Answer 2

Your question is missing its essential point:
Prove that a group H ... What??