If you directly connect the inverting and non-inverting inputs together you will almost certainly still get a non-zero (albeit small) output, due to the internal input offset voltage of the opamp (arising from chip manufacturing asymmetries) being multiplied by the opamp gain. You can add a small bias voltage, of appropriate polarity, to an input to compensate for the offset.
Transistor Switching that is used to sense high current and high voltage
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