Is a correlation matrix meaningful for a binary classification task? When examining my dataset with a binary target (y) variable I wonder if a correlation matrix is useful to determine predictive power of each variable.

My predictors (X) contain some numeric and some factor variables.
Well correlation, namely Pearson coefficient, is built for continuous data. Thus when applied to binary/categorical data, you will obtain measure of a relationship which does not have to be correct and/or precise.

There are quite a few answers on stats exchange covering this topic - this or this for example.