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Math Help - Help with proof: only element in a group with g^2=g

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    Help with proof: only element in a group with g^2=g

    Prove that if G is a group, then the only element g \in G such that g^2=g is 1.
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    Quote Originally Posted by didact273 View Post
    Prove that if G is a group, then the only element g \in G such that g^2=g is 1.
    Suppose that there is another element such that

    a^2=a Since G is a group a must have an inverse so multiply both sides by a inverse

    a^{-1}(a^2)=a^{-1}a \iff a=1
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