Prove that the product of two distinct flips within the dihedral group is a non-trivial rotation.
So this question is stating that if you have two different flips, that is the same thing as rotating the polygon by something non-zero. I know that if you flip a polygon twice, you get back to the original side, and since the flips are distinct, you can't flip twice without rotating in between. So you would flip, then do a non-trivial rotation, and then flip again. This is the same as just non-trivially rotating the original side. Is this on the right track for a proof of this? Is there anything extra I would need to say?