let be the element of given by
(1). Find and
and verify
(2). find the order of and
What is it that you do not understand about this question? It is a rather hard question to answer over the internet as it is about understanding, not about a simple `trick'. However, you should remember that what you are doing is the same as using a normal permutation. That is,
.
To multiply to disjoint cycles, you look at where the preceeding permutation takes the element you are looking at.
So, for example,
and all the rest are kept as they are, and so etcetera.
Does that make sense?
Now, to find the inverse of a (single) disjoint cycle, you should notice that if then you want in the inverse. This is equivalent to keeping the first element fixed and flipping all the others round,
.
Now, does that make sense?
It is now your task to apply all this to your question!