Linear Transformation Groups:

*  rotation: I = identity matrix is the identity element. det R=1
	Rotation is a member of the Special Orthogonal(n-dimensional) group.
	det R =+/- 1.  SO(n) member of Lie group.
*  (x1, x2, x3) -> (-x1, -x2, -x3) spatial inversion (parity). det R=-1
*  (x1, x2, x3) -> (x1, x2, -x3)   reflection. det R=-1