Yes, R3 can be zero but, for highest accuracy, R3 should equal the parallel equivalent impedance of R1 and R2. This is to compensate for the input bias currents of the inverting and non-inverting inputs to the op-amp. These bias currents are designed to be as low as possible but in some parts they are high enough that they should not be ignored. Each current must flow to the input through the part(s) connected, so it causes a small voltage drop across the components connected to the inputs. Balancing the values of these components between inputs causes the voltage drops to be equal and thus not appear as a differential voltage between the inputs, thus their effect is cancelled by the common mode rejection property of the op-amp.Now, since these bias currents are DC, they can only flow through DC paths. The only difference between the AC and DC amplifiers is the presence or absence of C, respectively. Since the DC impedance of C is infinite, it blocks any DC component from passing through the amplifier. This means that R1 can be ignored for this purpose and R3 should be set equal to R2. In the DC amplifier case, with C removed, R2 is now a path through which the inverting input's DC bias current can flow. So its resistance, along with the feedback resistor's, must be considered. Thus R3 should be set to the equivalent of R1 in parallel with R2. So, 1/R3 = 1/R1 + 1/R2. Rearranging, R3 = (R1 * R2)/(R1 + R2). (NOT R3=R1*R2 as you stated above.)Many modern op-amps have such small input bias currents that this compensation is not necessary and R3 may be set to 0 Ω. But if the input and feedback resistances are large, even a small bias current can cause significant error. The moral of this story, read the op-amp datasheets and calculate the voltage offset errors that will be caused by input bias currents (and subsequently amplified) and decide if they are acceptable or not.
