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Abstract Algebra/Group Theory/Group/Inverse is Unique
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Theorem
In a group, each element only has one inverse.
Proof
{|
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|0. Choose . Then, inverse g1−1 of g is also in G.
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|1. Assume g has a different inverse g2−1 in G
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2.
|| is associative on G
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3.
|| g1-1 and g2-1 are inverses of g on G (usage 3)
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4. , contradicting 1.
|| eG is identity of G (usage 3)
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