Question

Give an example of group elements a and b with the property that a^-1ba does not equal a.

Answer 1

Here's a nice example: think about the group {1,-1} under the usual multiplication. Let a=1 and b=-1. Then

\(a^{-1}ba = 1(-1)1 = -1 \neq a.\)

Answer 2

ah!!! Thanks!!