7.5 (part 2), due March 18

The rest of this section was pretty straightforward.  I thought it was very interesting that we could tell by the order of a group which group it was isomorphic to.  I got a little lost in the proof of the theorem that said that a group of order 6 was isomorphic either to Z_6 or S_3.  The origination of ba=(a^2)b and b^2=e was not really clear, but I got really confused when compared the correspondence to S_3. I didn't really follow that.  How did they know what each element of the group mapped to in S_3?