I have this problem... Let H = {B in S7 | B(2)=2 and B(5)=5}. Prove that H is a subgroup.

I have tried to do this by saying that the remaining cycle is a 5 cycle which is even...and I think I am way off base.

Is there anyone that can help get me started? I guess I just have to show non-empty, AB is in there and that B^-1 is in there, but truly, I am struggling with the permutation thing.

Thanks