We　investigate　the　stability　and　instability　of　the　magnetic　Rayleigh-Benard　problem　with　zero　resistivity.　A　stability　criterion　is　established,　under　which　the　magnetic　Benard　problem　is　stable.　The　proof　is　mainly　based　on　a　three-layers　energy　method　and　an　idea　of　magnetic　inhibition　mechanism.　The　stability　result　first　mathematically　verifies　Chandrasekhar＇s　physical　conjecture　in　1955　that　the　thermal　instability　can　be　inhibited　by　a　strong　(impressed)　magnetic　field　in　magnetohydrodynamic　(MHD)　fluids　with　zero　resistivity　(based　on　a　linearized　steady　magnetic　Benard　equations).　In　addition,　we　also　provide　an　instability　criterion,　under　which　the　magnetic　Rayleigh-Benard　problem　is　unstable.　The　instability　proof　is　mainly　based　on　a　bootstrap　instability　method　by　further　developing　new　techniques.　Our　instability　result　shows　that　the　thermal　instability　still　occurs　when　the　(impressed)　magnetic　field　is　weak.　(C)　2020　Elsevier　Masson　SAS.　All　rights　reserved.