Special affine group

In the mathematical study of transformation groups, the special affine group is the group of affine transformations of a fixed affine space which preserve volume. This is the affine analogue of the special linear group.
On Rn, every special affine transformation has the form
where "A" is an "n"×"n" matrix of determinant one, and b is a fixed vector in Rn. The special affine group is a subgroup of the affine group.