  We use the AdS/CFT correspondence to study first-order relativistic viscous
magneto-hydrodynamics of (2+1) dimensional conformal magnetic fluids. It is
shown that the first order magneto-hydrodynamics constructed following Landau
and Lifshitz from the positivity of the entropy production is inconsistent. We
propose additional contributions to the entropy motivated dissipative current
and, correspondingly, new dissipative transport coefficients. We use the
strongly coupled M2-brane plasma in external magnetic field to show that the
new magneto-hydrodynamics leads to self-consistent results in the shear and
sound wave channels.
