Proof

Since every permutation in S_n can be written as a product of disjoint cycles, it suffices to show that every cycle is a product of 2-cycles.

For every m-cycle (a₁, ..., a_m) we have

(a₁, ..., a_m) = (a₁, a₂) (a₂, a₃) ··· (a_{m - 1},a_m),

and the proof is complete.