The output sign is the direction needed to balance current at the inverting node. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The input pin current is zero

The input pin takes zero current, so the node balance is resistor-in equals feedback-out.

Ipin=0 AI_{\text{pin}} = 0\ \text{A}
Zero input pinThe op-amp input current is pinned to zero.+-op amprails -12 V to 12 VVout -6 VV+ 0 VV- 0 VI+ 0 AI- 0 ARin 2 ohmIin 1 ARf 6 ohmIf 1 AV+ = V-inverting

Feedback current matches input current

The checked current is 1 ampere in and 1 ampere back through feedback.

Iin=Ifeedback=1 AI_{\text{in}} = I_{\text{feedback}} = 1\ \text{A}
KCL at the inverting nodeThe displayed resistor currents are the checked node balance.+-op amprails -12 V to 12 VVout -6 VV+ 0 VV- 0 VI+ 0 AI- 0 ARin 2 ohmIin 1 ARf 6 ohmIf 1 AV+ = V-inverting