Prove that the set of all indirect isometries (reflections and glide reflections) is not a group.

I kind of have an idea that "having the Identity in the set" part of the definition of a group should be used to disprove it but I am having trouble formalising the proof. Any help would be really appreciated!

Thanks!

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Edit: Now that the OP has figured it out, I should point out that this is what people refer to when they say a group should be "closed under its operation." I avoided this term, because I hate that this phrase is often included as a group axiom: a group operation is defined to be map $G\times G\to G$, so of course its image is in $G$. But here's an example where the operation takes you outside the underlying set, so the set is not closed under the operation.