  We investigate the stability and instability of the magnetic
Rayleigh--B\'enard problem with zero resistivity. An stability criterion is
established, under which the magnetic B\'enard problem is stable. The proof
mainly is based on a three-layers energy method and an idea of magnetic
inhibition mechanism. The stable result first mathematically verifies
Chandrasekhar's assertion in 1955 that the thermal instability can be inhibited
by strong magnetic field in magnetohydrodynamic (MHD) fluid with zero
resistivity (based on a linearized steady magnetic B\'enard equations). In
addition, we also provide an instability criterion, under which the magnetic
Rayleigh--B\'enard problem is unstable. The proof mainly is based on the
bootstrap instability method by further developing new analysis technique. Our
instability result presents that the thermal instability occurs for a small
magnetic field.
