In an ideal operational amplifier (op-amp), the output voltage is determined by the difference in the input voltages, multiplied by the gain. However, the op-amp in this case has an offset voltage of 1 mV.
Given the offset voltage, the output will be directly proportional to this offset and the gain set by the feedback network. In this case, the op-amp is ideal in all respects other than the offset voltage, and this will result in an output voltage of approximately $\pm$1 V.
Thus, the output voltage is closest to $\pm$1 V.