This article presents two key computations in MW-motivic cohomology. Firstly, we compute the MW-motivic cohomology of the symplectic groups Sp2n 2n for any n is an element of N using the Sp- orientation and the associated Borel classes. Secondly, following the classical computations and using the analogue in A 1-homotopy of the Leray spectral sequence, we compute the ?7-inverted MW-motivic cohomology of general Stiefel varieties, obtaining in particular the computation of the ?7-inverted MW-motivic cohomology of the general linear groups GLn n and the special linear groups SLn n for any n is an element of N. Finally, we determine the multiplicative structures of these total cohomology groups.