3. Composite Transformations

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$sr = u$

$$(1, 2, 3) \quad \mapsto \quad (1, 3, 2) \quad \mapsto \quad (2, 1, 3) \quad = \quad u$$

 

$rs = t$

$$(1, 2, 3) \quad \mapsto \quad (3, 1, 2) \quad \mapsto \quad (3, 2, 1) \quad = \quad t$$

 

$r^2s = u = sr$

$$(1, 2, 3) \quad \mapsto \quad (2, 3, 1) \quad \mapsto \quad (2, 1, 3) \quad = \quad u$$

 

$sr^2 = t = rs$

$$(1, 2, 3) \quad \mapsto \quad (1, 3, 2) \quad \mapsto \quad (3, 2, 1) \quad = \quad t$$