I've trying to understand inverse's in permutations, so consider the permutation $T$ given by:
$T =\begin{pmatrix} 1 & 2 & 3 & 4 & 5\\ 3& 2 & 4 & 5 & 1 \end{pmatrix}$ then $T^{-1}=\begin{pmatrix} 1 & 2 & 3 & 4 & 5\\ 5& 2 & 1 & 3 & 4 \end{pmatrix}$ would be it's inverse. But, I was wonder is it possible to have a permutation that isn't it's own inverse or is every permutation its own inverse?