I want to know the answer to the following question:
When is it preferable to consider two group elements to be the same?
All the background I'm provided with is that "For example, in D4 above, once a reflection is performed, the square never gets back to the r2 configuration by just applying the rotation operations (and no further reflections), i.e. the rotation operations are irrelevant to the question whether a reflection has been performed.". Is that enough to answer the question?
Answer: yes