So I have ata^-1=at(n)

because a^-1 sends a(1)--->1,a(2)--->2,.....a(n)--->n

By defininition of t, we have a(1), a(2), a(3)...a(k). We go to k because our definition of t says k<=n.

For b,

Let b be any cycle of length k.

We have (1,2.....k). I'm not sure how to show the rest.