In a multiple regression analysis, B, along with several other predictors, was found to be a predictor of A. Literature also says B is a predictor of A.

Since A and B are significantly correlated, I am wondering: can A also be one of the predictors of B? When running a multiple regression analysis for B, should A be added to the model as one of the potential predictors?

(In literature, no one has tested whether A is a predictor of B.)