It's a tie because both responses correctly derive the exact gain formula Av = –R2/R1 for the visible inverting op-amp circuit shown in the image, use the same ideal-op-amp assumptions, apply Kirchhoff’s current law properly, and present the final result clearly with no factual errors or omissions.

Both responses arrive at identical conclusions because they successfully calculate the precise gain formula Av = -R2/R1 for the inverting operational amplifier circuit displayed in the provided diagram. Each analysis employs the standard assumptions that define an ideal op-amp, including infinite input impedance, zero input bias current, and the virtual short concept where both input terminals maintain the same voltage potential. The mathematical approaches in both responses demonstrate proper application of Kirchhoff's current law, systematically analyzing the current flow through the feedback resistor R2 and input resistor R1. This fundamental circuit analysis technique allows both solutions to methodically work through the voltage and current relationships that govern the inverting amplifier's behavior. Furthermore, both responses deliver their conclusions with exceptional clarity, presenting the negative gain relationship in a straightforward manner that accurately reflects how this classic op-amp configuration produces an output signal that is both amplified and inverted relative to the input. Neither response contains any technical inaccuracies, mathematical errors, or gaps in reasoning, making them equally valid and complete derivations of this fundamental electronics principle.