  We study the tamed magnetohydrodynamics equations, introduced recently in a
paper by the author, perturbed by multiplicative Wiener noise of transport type
on the whole space $\mathbb{R}^{3}$ and on the torus $\mathbb{T}^{3}$. In a
first step, existence of a unique strong solution are established by
constructing a weak solution, proving that pathwise uniqueness holds and using
the Yamada-Watanabe theorem. We then study the associated Markov semigroup and
prove that it has the Feller property. Finally, existence of an invariant
measure of the equation is shown for the case of the torus.
