If $ belongs to Sn (where Sn is the symmetric group of degree n), show that $^2 = % if and only if $ is a product of disjoint transpositions.
Here % should mean the unit 1.
If $ is a product of disjoint transpositions, then $=a1*a2...*ak, where ai are ...
A proof involving symmetric groups and disjoint transpositions is provided. The proof is concise.