  This paper is concerned with the vanishing viscosity and magnetic resistivity
limit for the two-dimensional steady incompressible MHD system on the half
plane with no-slip boundary condition on velocity field and perfectly
conducting wall condition on magnetic field. We prove the nonlinear stability
of shear flows of Prandtl type with nondegenerate tangential magnetic field,
but without any positivity or monotonicity assumption on the velocity field. It
is in sharp contrast to the steady Navier-Stokes equations and reflects the
stabilization effect of magnetic field. Unlike the unsteady MHD system, we
manage the degeneracy on the boundary caused by no-slip boundary condition and
obtain the estimates of solutions by introducing an intrinsic weight function
and some good auxiliary functions.
