Portfolio Management-correlation

I recently got an incorrect answer on a PM Qbank question on the CML. It was incorrect because it said that the correlation between the risk free asset and the risk asset is 1. Graphically it makes since because of the linear relationship but it does not seem possible mathematically since the standard deviation of the risk free asset is 0. r=cov/s1*s2. If one of the inputs in the denominator is 0 would r have to = 0?

well mathetically r can’t equal zero; r would simply be undefined.

I agree. r is about two random quantities.