Inverse of the product of two elements of a monoid ↩

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created: 2022-11-12 20:47:03
modified: 2022-11-12 21:00:11

Statement: Let

be a monoid or group with identity element

and let

and

be invertible elements of

, where

and

are the inverses. Then is invertible and its inverse is given by

Proof

By using associativity and that is the identity element:

Also:

Since both evaluate to , QED.