To show that you need to show that (identity permuation) and that if . Also it would be helpful to write (you will see why) instead.

First we show that is the identity permuation. This means we need to show for all . We can assume that because otherwise and so there is no need to check that case. Remember that (this is why we rewrote the indicies differently). Therefore, . If we want it must mean that . Therefore, the smallest such is and so .

Compare .2. Prove that Sn is non-abelian if n is greater than or equal to 3.