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Proposition: Uniqueness of Inverse Elements
Let $(X,\ast)$ be an algebraic structure with an associative binary operation $[\ast".$ Let $x\in X$.
If an inverse element of $x$ exists then it is unique.
Notes
 This proposition holds in all algebraic structures, in which the existence of inverse elements is postulated.
 Thus, the proof is the same for groups, unit rings, and fields.
Table of Contents
Proofs: 1
Mentioned in:
Definitions: 1 2 3
Proofs: 4 5 6
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