Output resistance of non-inverting amplifier
Your analysis will work when the output is forced to 1V instead of 0V. I was able to get the correct answer (output impedance is indeed lowered by loop gain!) by analyzing a 1V voltage source on the output.

The way that I prevent this sort of mistake is by being strict about how I write my equations. Among other rules, I don't introduce new terms like L and b, I don't use any numbers until the end, and I don't make approximations in the algebra. When the algebra becomes tedious, I use the Maxima computer algebra program. I think there is also a Mathematica package somewhere that does this type of analysis correctly.

In this problem, the rule that was violated is that the Vout term was replaced by a number before the equations were solved. In this case the number choice was unfortunate and it ruined the equation.

The more intuitive explanation is that Zout=Vout/Iout, so Vout=0 is a problematic choice.