Inverses

An element is invertible under an operation if it has a left inverse and a right inverse.

In the common case where the operation is associative, the left and right inverse of an element are equal and unique. Indeed, if and are respectively a left inverse and a right inverse of , then
:

The inverse of an invertible element is its unique left or right inverse.

If the operation is denoted as an addition, the inverse, or additive inverse, of an element is

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