Let X and Y be r × s and s × r matrices. In this paper we study varieties defined by the matrix equation XY = I . We call these varieties generalised affine Stiefel algebraic varieties. We show that the canonical divisor of these varieties is Cartier using two different methods. The main aim is to characterise the canonical divisor of these varieties in terms of group representations. Affine Stiefel algebraic variety is a special case of the generalised affine Stiefel algebraic varieties.