Is it true that for Cobb-Douglas preferences, the demand function is always iso-elastic? As we know that $Q*P=const.$ for Cobb-Douglas preferences, we can thus conclude that $\frac{dQ/Q}{dP/P}$ is always $-1$:
$$
QP=const. \implies 0=d(PQ)=Q\ dP+P\ dQ \implies \frac{dQ}{Q}=-\frac{dP}{P}
$$
Yes.
I have to include at least 30 characters in an answer, so let me repeat: Yes.