It　is　still　open　whether　the　inhibition　phenomenon　of　the　Rayleigh-Taylor　(RT)　instability　by　a　horizontal　magnetic　field　can　be　mathematically　verified　for　a　non-resistive　magnetohydrodynamic　(MHD)　fluid　in　a　two-dimensional　(2D)　horizontal　slab　domain,　since　it　was　roughly　verified　in　the　linearized　case　by　Wang　in　[43].　In　this　paper,　we　show　that　this　inhibition　phenomenon　can　be　rigorously　verified　in　the　(nonlinear)　inhomogeneous,　incompressible,　inviscid　case　with　velocity　damping.　More　precisely,　we　show　that　there　is　a　critical　number　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　exponentially　stable　in　time.　Moreover,　we　also　provide　a　nonlinear　instability　result　for　the　case　|m|　is　an　element　of　(0,　mC).　Our　instability　result　reveals　that　a　horizontal　magnetic　field　can　not　inhibit　the　RT　instability,　if　it＇s　strength　is　too　small.　(c)　2022　Elsevier　Inc.　All　rights　reserved.