Let S be a finite symmetric subset of GL(n,F), F an arbitrary field, satisfying |S^3| < K|S| for some K > 1. Then there are normal subgroups P _< G of , such that G/P is soluble, P is a finite perfect group contained in S^6 and S is contained in the union of K^c(n) cosets of G, where c(n) depends only on n. This includes the Product Theorem for finite simple groups of bounded rank proved by Breuillard-Green-Tao and Pyber-Szabo and various other earlier results.