As it was already stated, a (proper) rotation is different from an arbitrary fixed-point motion in its preservation of the orientation of the vector space. Thus, the determinant of a rotation orthogonal matrix must be 1. The only other possibility for the determinant of an orthogonal matrix is , and this result means the transformation is a hyperplane reflection, a point reflection (for odd ), or another kind of improper rotation. Matrices of all proper rotations form the special orthogonal group.