Does there exist a math operator that denotes to take the inverse of something?

Question

I’m familiar of the inverse function notation, but I was wondering if there exists a math operator that denotes to take the inverse of something.

Answer 1

If the inverse is always unique, then such an operation is often denoted by $$(\cdot)^{-1}.$$

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NB: Here the dot (i.e., $\cdot$) is a sort of placeholder. It is fairly standard. What one infers from it is that one plugs an element of the domain of the operation into the place where the dot is, often omitting the brackets (that are still implied if not written); for instance, for any group $G$, we have this: $$\begin{align} (\cdot)^{-1}: G & \to G, \\ g & \mapsto g^{-1}.\end{align}$$

NB2: Sometimes inverses are not uniquely defined. See here for an example. The inverse operation is thus undefined in these instances.