Invertible element

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This article defines a property of elements or tuples of elements with respect to a binary operation

Further information: inverse element

Definition

An element a in a set S with binary operation * and neutral element e is termed:

Note that we need to be particularly careful here. If an element possesses both a left inverse and a right inverse, that does not necessarily guarantee that the element possesses a two-sided inverse. The guarantee can, however, be given in the case of associativity. For full proof, refer: Inverse element#Equality of left and right inverses