Noting that any identity matrix is a rotation matrix, and that matrix multiplication is associative, we may summarize all these properties by saying that the rotation matrices form a group, which for is non-abelian, called a special orthogonal group, and denoted by , , , or , the group of rotation matrices is isomorphic to the group of rotations in an space. This means that multiplication of rotation matrices corresponds to composition of rotations, applied in left-to-right order of their corresponding matrices.
