Question 338155
To find the inverse of any permutation, simply write the elements in reverse order. In your case, the inverse of (1 2 3 4 5) is (5 4 3 2 1). It's perfectly possible to shift the elements, just as long as you do so in a consistent manner. So if we shift EVERY element to the right one place (the 1 will loop back to the beginning), we then get (1 5 4 3 2).



So (5 4 3 2 1) = (1 5 4 3 2) (ie they are the same permutation) is the inverse of (1 2 3 4 5)



It turns out that every permutation has an inverse. This is due to the fact that permutations form a group.