Context: 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). The subgroup test is a necessary and sufficient condition for a subset H of a group G to be a subgroup: it is sufficient to check that g−1h ∈ H for all elements g, h ∈ H. Knowing the subgroups is important in understanding the group as a whole.d[›]

Question: What is composed of two rotations?
Answer: a rotation

Question: What rotation can a rotation be reversed by?
Answer: inverse

Question: What essential condition must be met for a subset of a group to be a subgroup?
Answer: The subgroup test

Question: What is defined when moving in the opposite direction?
Answer: Unanswerable

Question: 270 for 180 is an example of what kind of rotation?
Answer: Unanswerable

Question: subgroup R is made up of the inverse and what?
Answer: Unanswerable

Question: What is unimportant for understanding the group as a whole?
Answer: Unanswerable

Question: Knowing the group as a whole is important for understanding what?
Answer: Unanswerable