For which sets Adoes there exist a bijection from A to A that is different from the identity function of A?

Answer 1

Let A be any set that has at least 2 elements and let every element in set A maps to itself except for 2 elements that do not map to each other. i.e.

A = 1, 2, 3, ... , n

1 --> 2

2 --> 1

3 --> 3

4 --> 4

...

n --> n