Power of Product of Commutative Elements in Semigroup/Examples/Elements of 3rd Symmetric Group

Examples of Use of Power of Product of Commutative Elements in Semigroup
Let $S = \set {1, 2, 3}$.

Let $S_3$ denote the symmetric group on $3$ letters.

Let $\rho, \sigma \in S_3$ defined in two-row notation as:

Then:
 * $\rho^2 \sigma^2 \ne \paren {\rho \sigma}^2$