Calculating the loop gain for an ideal op-amp with time delay
Below is the open loop circuit without feedback.



We know that since this is an ideal op-amp, \$V_+ = V_- = 0V \$. When we do KCL at the inverting terminal, we get \$|V_{out}/V_{in}| = 1/(sCR)\$.

Now we know this is the open loop voltage gain, or \$A\$. 
When we add feedback, our feedback term is \$\tau = e^{-s\tau}\$. The first order approximation for this is \$(1-s\tau/2)/(1+s\tau/2) \$. 



The feedback term represents \$B \therefore AB=[(1/(sCR)*(1-s\tau/2)/(1+s\tau/2))]\$. AB is the loop gain.