We present an energy, cross-helicity and magnetic helicity preserving method for solving incompressible magnetohydrodynamic equations with strong enforcement of solenoidal
constraints. The method is a semi-implicit Galerkin finite element discretization, that enforces
pointwise solenoidal constraints by employing the Scott-Vogelius finite elements. We prove the
unconditional stability of the method and the optimal convergence rate. We also perform several
numerical tests verifying the effectiveness of our scheme and, in particular, its clear advantage
over using the Taylor-Hood finite elements.