Editing Inverse element (section)

==In groups==
A [[group (mathematics)|group]] is a [[set (mathematics)|set]] with an [[associative operation]] that has an identity element, and for which every element has an inverse. 

Thus, the inverse is a [[function (mathematics)|function]] from the group to itself that may also be considered as an operation of [[arity]] one. It is also an [[involution (mathematics)|involution]], since the inverse of the inverse of an element is the element itself.

A group may [[group action|act]] on a set as [[transformation (mathematics)|transformations]] of this set. In this case, the inverse <math>g^{-1}</math> of a group element <math>g</math> defines a transformation that is the inverse of the transformation defined by <math>g,</math> that is, the transformation that "undoes" the transformation defined by <math>g.</math>

For example, the [[Rubik's cube group]] represents the finite sequences of elementary moves. The inverse of such a sequence is obtained by applying the inverse of each move in the reverse order.