  In this note we investigate Liouville type theorems for the steady three
dimensional MHD and Hall-MHD equations, and show that the velocity field $u$
and the magnetic field $B$ are vanishing provided that $B\in
L^{6,\infty}(\mathbb{R}^3)$ and $u\in BMO^{-1}(\mathbb{R}^3)$, which state that
the velocity field plays an important role. Moreover, the similar result holds
in the case of partial viscosity or diffusivity for the three dimensional MHD
equations.
