1.
if a,b are in G, b^6=e and ab=b^4a, prove b^3=e and ab=ba
Solution
ab=b^4a
multiply with b^2 on both sides
=>ab^3 = b^6 a
=> b^3 = b^6
given b^6 = e
=> b^3 = e
ab = b^4 a
mutiply and divide by b^3

2.
= b ^7 a / b^3
= b^6 (ba) / b^3
= e (ba) / e
= ba