Is there a name for functions that are their own inverses

There are terms for various kinds of functions (or operators) such as...

associative - (a # b) # c  =  a # (b # c)
commutative - a # b  =  b # a
idempotent  - f (f (x)) = f (x)


Is there a similar name for functions that are their own inverse?

f (f (x)) = x

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2 Answers

It is called as an involution.

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Thanks - have to wait a few minutes before I can accept, but this is the answer. –  Steve314 Sep 27 '13 at 17:05
Some examples of involutions are shown here –  Mufasa Sep 27 '13 at 17:08
The most trivial involution is f(x) = x. –  Tortoise Sep 27 '13 at 23:00

Such a function is called an involution.

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