# Thread: Inverse Isometry Proof Hint Help

1. ## Inverse Isometry Proof Hint Help

Hi I've been given the following exercise:

Let FGH be the composite of three isometries. Assume that there inverses exist. Prove that (FGH)^-1 exists, and express this inverse in terms of the inverses of the individual isometries.

I would greatly appreciate any hint about where to start and any general advice about attempting to solve problems of this sort. I need to rewire my brain, and I can't quite get it yet.

Thanks,
Ultros

2. Haven't really done isometry, but assuming it is a little like group theory...

Presumably the inverse is

H^-1G^-1F^-1...

This exists since the inverse of F,G and H exists, and thus the composition exists.

Prove that it is actually an inverse by sticking it before FGH and showing you get the identity element.