assume terminal A is at 5V. clearly higher than terminal B's 1V. if A is the inverting input, then the opamp's output should go as low as possible -- preventing the transistor from turning on at all. This is a stable state. Likewise, if A were 0V, and B were 1V, then the opamp would force as much current into the base as it could, turning the transistor on fully -- again a stable state. indeed, this would be a latch.
Now assume in the 5v/1v example that A were non-inverting. the transistor would turn on, forcing the terminal away from 5V. Likewise in the 0v/1v case, the transistor would turn off allowing the voltage to rise. This would be the correct action.