Exercise 3, § 3

Let $A$ be a right coherent ring ($§ 2$, Exercise 12). For a product of left $A$-modules to be faithfully flat, it is sufficient that each of them be flat and that at least one of them be faithfully flat.

Deduce that, if $A$ is a coherent commutative ring, the ring of formal power series $A[[X_1, \ldots, X_n]]$ is a faithfully flat $A$-module.