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Prove that all rotations and translations form a subgroup of the group of all reflections and...

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Advance Math

Prove that all rotations and translations form a subgroup of thegroup of all reflections and products of reflections in EuclideanGeometry. What theorems do we use to show that this is asubgroup?

I know that I need to show that the subset is

closed

identity is in the subset

every element in the subset has an inverse in the subset.

I don't have to prove associative property since that is alreadyproven with Isometries. What theorems for rotations andtranslations so that they are closed, identity is in the subset andevery element is the subset has an inverse in the subset.

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