# What information VIF can provide but correlation matrix cannot in detecting multicollinearity?

In multiple linear regression, the correlation matrix of predictors already clearly indicates the strength of correlation between any two predictors. Why do we use any other tools, such as VIF, to check the existence of multicollinearity?

Here's a particular example: suppose you are trying to model/predict based on a set of compositional variables, i.e. you know the strength of someone's preferences brand A or brand B or brand C or brand D ... or brand Z, which add up to 1 overall (by definition/construction), and you want to use "prefers brand *" as a set of predictors in the same model. Preferences for particular pairs of brands may be either positively or negatively correlated, but overall the set of predictors contains only 25, not 26, pieces of information. So the correlation between $(A+B+\ldots+Y)$ and $Z$ (or between any preference and the sum of all of the other preferences) is exactly -1, even though the correlations of particular brand preferences with $Z$ can be all over the place.