Question: Show that the presentation (a, b : a 3 = 1, b 2 = 1, ba = a 2 b) of Exercise 10 gives (up

Show that the presentation (a, b : a³ = 1, b² = 1, ba = a²b) of Exercise 10 gives (up to isomorphism) the only nonabelian group of order 6, and hence gives a group isomorphic to S_3.

Data from Exercise 10

Show, using Exercise 13, that (a, b: a³ = 1 b² = 1, ba = a²b) gives a group of order 6. Show that it is nonabelian.

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