Q.How can you use an op amp to invert a signal?

The inverting amplifier is the most basic linear op-amp circuit. The input voltage $V_i$ is applied through an input resistor $R_i$ to the inverting $(-)$ terminal, the non-inverting $(+)$ terminal is grounded, and a feedback resistor $R_f$ connects the output back to the inverting terminal.

Analysis uses the virtual ground: with negative feedback the inverting node sits at $0\ \text{V}$, and no current enters the op-amp input. The current through the input resistor, $V_i/R_i$, must therefore flow on through the feedback resistor. Equating these currents gives the output voltage and gain:

The negative sign shows the output is inverted — it is $180^\circ$ out of phase with the input — and the gain magnitude is set entirely by the resistor ratio, not by the op-amp itself. This makes the gain precise and stable. …