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.