How can we prove that any bijection from any set to itself is a composition of 2 involutions ?
So I know that any involution is a bijection, and so it has an inverse (which happens to be itself here). Also, I was thinking that maybe we could use the identity function on the set somehow because the identity function is also an involution right ?
Also the case where the bijection in the question is already an involution is trivial since we can take the composition of itself with the identity.
Thanks for your help.