The steady magnetohydrodynamic stagnation point flow and heat transfer over a stretching/shrinking surface in a hybrid nanofluid with partial slip and viscous dissipation were theoretically/numerically studied. The governing equations of the problem were turned into ODEs by using appropriate transformations. The plots of most important parameters were presented for both surfaces. It was found that on increasing the magnetic parameter, the hybrid nanofluid is better as a heater rather than nanofluid, however, it is better as a cooler on rising Eckert number, the stretching and slip parameters. For shrinking sheet, critical regions of unique/dual solution have been introduced. Further, stability of the unique/dual solution was studied where three regions of stability were noticed. It was deduced that the velocity and temperature are sensitively available close to the terminated line in the dual solution region. It was also proved that their behavior is absolutely different over the three regions of stability. (C) 2020 Elsevier B.V. All rights reserved.