I want to know the answer to the following question:
What essential condition must be met for a subset of a group to be a subgroup?
All the background I'm provided with is that "In the example above, the identity and the rotations constitute a subgroup R = {id, r1, r2, r3}, highlighted in red in the group table above: any two rotations composed are still a rotation, and a rotation can be undone by (i.e. is inverse to) the complementary rotations 270° for 90°, 180° for 180°, and 90° for 270° (note that rotation in the opposite direction is not defined).". Is that enough to answer the question?
Answer: no