Every element of a group has exactly one inverse ↩

Metadata

aliases: [Every element of a group has a unique inverse, Left and right inverses in monoids are the same]
shorthands: {}
created: 2021-11-05 22:54:40
modified: 2022-11-12 02:27:49

Statement: every

element of a group

has exactly one inverse

Proof

Suppose that and are both inverses of . Then

So , there really is only one inverse of .

Notes

This also implies that if an element of a monoid has both a left and a right inverse, then they are the same