Let $a,\,b,\,c$ be elements of some group with $abc=e$. Does it follow that $bca=e$? And does it follow that $bac=e$? Give proof or counterexample.
If $abc=e$ then $bc= a^{-1}$ then it follows that $bca= (a^{-1})a=e$. But how about $bac=e$? Can someone help me. I'm self learning the fundamentals of abstract algebra.