Abstract Algebra: Solving Stumping Questions | αη = β and G is Abelian

[m-chan]

I have 2 algebra questions which are stumping me, I just can't seem to use my notes to figure them out!

1. Let α, β ∈ S17 where α = (17 2)(1 2 15 17 ), β = (2 3 16)(6 16 17 ).
Determine η, as a product of disjoint cycles, where αη = β.

2. Let G be a group in which a^2 = 1 for all a ∈ G. Prove that G is Abelian.
Hint: Consider (ab)^2.

HELP PLEASE :(

 

[Mark44]

For 2, consider what (ab)² equals.

 

[m-chan]

Right, I've figured out 2, thanks Mark44 and I've done some of 1, but I'm stuck at the end of the question.

I have η= (2 17)(17 15 2 1)(2 3 16)(6 16 17), but I'm not sure if that's right though. I also don't know where to go from there.