Group (mathematics)
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 270deg for 90deg, 180deg for 180deg, and 90deg for 270deg (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[>]
What rotation can a rotation be reversed by?
inverse
is inverse to) the complementary rotations 270deg for 90deg, 180deg for 180deg, and 90deg for 270deg (note that rotation in the opposite direction is not defined).
a rotation