Detecting reflection in non-orthogonal rotation

I've known that, in orthogonal rotation, if the rotation matrix has determinant of -1 then reflection is present. Otherwise the determinant is +1 and we have pure rotation. May I extend this "sign-of-determinant" rule for non-orthogonal rotations? Such as orthogonal-into-oblique axes or oblique-into-orthogonal axes rotations? For example, this matrix

 .9427   .2544   .1665   .1377
-.0451  -.0902  -.9940  -.0421
.3325   .3900   .1600   .8437
.4052   .8702   .2269   .1644


is an oblique-to-orthogonal rotation (I think, because sums of squares in rows, not in columns, are 1). Its determinant is -0.524. May I state that the rotation contains a reflection? Thanks in advance.

• I just deleted my answer to reduce unnecessary noise. Thanks for your comment. – suncoolsu Mar 14 '11 at 13:11