Suppose that the correlation between and and the correlation between and are both the same number . Then lies between and , the light blue shaded region below.
If they’re fully correlated, , then, of course, is also 1. But as decreases from 1, the minimum value for decreases four times as fast. If , then could be almost as low as . With , and could be uncorrelated.
The only constraint on a correlation matrix, knowing nothing else is that . For three variables with correlations s,t,r this leads to the inequality