Inverse

The notion of inverse in mathematical operation is simply the anti-operator.

Excerpt from Wikipedia

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Compositional inverseInverses and composition

If $f$ is an invertible function with domain $X$ and codomain $Y$, then

$f^{-1}\left(\,f(x)\,\right)=x$, for every $x\in X$; and $f\left(\,f^{-1}(y)\,\right)=y$, for every $y\in Y.$.

Using the composition of functions, we can rewrite this statement as follows:

$f^{-1}\circ f=\operatorname {id} _{X}$ and $f\circ f^{-1}=\operatorname {id} _{Y},$

where $\operatorname {id} _{X}$ is the identity function on the set $X$; that is, the function that leaves its argument unchanged. In Category Theory, this statement is used as the definition of an inverse morphism.