Output impedance of a series shunt feedback amplifier
Here is my solution:

1.) Apply a test voltage Vin between both output nodes. This voltage causes two currents - one current i1 directly into the amplifier (through ro) and another current through the feedback network producing a voltage (Vn=Vin*beta) at the opamp input. Of course, the "actual" input signal Vi is set to zero!

2.) The input voltage Vn will be amplified by the gain (-A) and drives another current i2 through the output resistor ro (Ohms law).

3.) Both currents may be superimposed (added together) because we assume of course linearity. Both currents have the same direction (inverting gain) and the sum (i=i1+i2) leads to a very small output resistance rout=Vin/i.