The Alfv\'en waves are fundamental wave phenomena in magnetized plasmas. Mathematically, the dynamics of Alfv\'en waves are governed by a system of nonlinear partial differential equations called the MHD equations. In this talk, we will focus on the rigidity aspect of the scattering problem for three-dimensional MHD equations. We will prove a couple of rigidity theorems that the Alfv\'en waves must vanish identically if their scattering fields vanish at infinities. This is consistent with the physical intuition that there are no Alfv\'en waves at all emanating from the plasma if no waves are detected by the far-away observers.