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