Using appropriate figures, show that the group S₃ is not commutative.

To show that the group \( S_3 \) (the symmetric group on 3 elements) is not commutative, we need to demonstrate that there exist two elements \( \sigma \) and \( \tau \) in \( S_3 \) such that \( \sigma \tau \neq \tau \sigma \).

The group \( S_3 \) consists of all the permutations of three elements. The elements of \( S_3 \) are: 

\[
\{ e, (12), (13), (23), (123), (132) \}
\]

where \( e \) is the identity permutation, \( (12) \), \( (13) \), and \( (23) \) are the transpositions, and \( (123) \), \( _____ __________ ________ ____ __________ ________ ____ __________ ______ ______ ________ ___.
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