Question

In my book it says that because ab =/=ba, the immdeiate consequence is that aba=/=b. How did they come up with this? Background info: There is a group with 2 elements of order 2, so a^2=e and b^2=e.

Answer 1

Oh i see it now, aba=/=b, becuase ab=/=ba, if ab=ba, then aba=b, becuase we could rewrite aba as aab=eb=b