We　investigate　whether　the　inhibition　phenomenon　of　the　Rayleigh-Taylor　(RT)　instability　by　a　horizontal　magnetic　field　can　be　mathematically　verified　for　a　non-resistive　viscous　magnetohydrodynamic　(MHD)　fluid　in　a　two-dimensional　(2D)　horizontal　slab　domain.　This　phenomenon　was　mathematically　analyzed　by　Wang　(J.　Math.　Phys.,　53:073701,　2012)　for　stratified　MHD　fluids　in　the　linearized　case.　To　our　best　knowledge,　the　mathematical　verification　of　this　inhibition　phenomenon　in　the　nonlinear　case　still　remains　open.　In　this　paper,　we　prove　such　inhibition　phenomenon　for　the　(nonlinear)　inhomogeneous,　incompressible,　viscous　case　with　Navier　(slip)　boundary　condition.　More　precisely,　we　show　that　there　is　a　critical　number　of　the　field　strength　mC,　such　that　if　the　strength　|m|　of　a　horizontal　magnetic　field　is　bigger　than　mC,　then　the　small　perturbation　solution　around　the　magnetic　RT　equilibrium　state　is　algebraically　stable　in　time.　Moreover,　we　also　provide　a　nonlinear　instability　result　when　|m|　∈　[0,mC).　©　2023　Global-Science　Press.