For the first part, let and start taking products of until you see a pattern. Notice that . Similarly, . I think you can take it from here.

For the second part, let . Then, if e is the identity,

for n copies of ab

by associativity (notice that you have n copies of ba)

by cancellation

If , then .

So, .

By associativity, .

By cancellation, , which is a contradiction.

Thus, .