Your representation $p$ is not faithful, since we have $$ ABA^{-1}BA^{-1}BAB^{-1}ABA^{-1}BA^{-1}BAB^{-1}ABA^{-1}BA^{-1}BAB^{-1} \ = \ 1. $$
Stefan Kohl
- 19.6k
- 21
- 75
- 137