  This article is concerned with the global exact controllability for ideal
incompressible magnetohydrodynamics in a rectangular domain where the controls
are situated in both vertical walls. First, global exact controllability via
boundary controls is established for a related Els\"asser type system by
applying the return method, introduced in [Coron J.M., Math. Control Signals
Systems, 5(3) (1992) 295--312]. Similar results are then inferred for the
original magnetohydrodynamics system with the help of a special pressure-like
corrector in the induction equation. Overall, the main difficulties stem from
the nonlinear coupling between the fluid velocity and the magnetic field in
combination with the aim of exactly controlling the system. In order to
overcome some of the obstacles, we introduce ad-hoc constructions, such as
suitable initial data extensions outside of the physical part of the domain and
a certain weighted space.
