Consider the following permutation f in S6:
f = 1 2 3 4 5 6
.....6 1 3 5 4 2
(The above is one set all in parentheses...)
Calculate f^-1
How do I do this?
Yes, that is fine. You could also write your group in the cycle notation as a product of disjoint cycles $\displaystyle f=(1,6,2)(4,5)$. In this notation it's preferred not to write cycles that have only one entry. Any missing element is mapped to itself.
$\displaystyle f^{-1}=(1,6,2)^{-1}(4,5)^{-1}=(2,6,1)(5,4)$.
which is the same as your answer in array notation.