Prove that an element has order $2$ in $S_n$ if and only if its cycle decomposition is a product of commuting $2-$cycles.
I know the proof or how to solve it. But I am interested in how the disjoint cycle decomposition of these order $2$ elements is carried out.
In $S_n$, $(1, 2)$ is a order $2$ element. But what will be its product of disjoint $2-$cycle decomposition?
Any help is appreciated. thanks.