Prove that M is flat if and only if each $M_i$ is flat.

Question

Let $\{M_i\}_{i \in I}$ be any family of $A$-modules, and let $M$ be their direct sum. Prove that M is flat if and only if each $M_i$ is flat.

Comments:

I'm taking a homomorphism $f: N \longrightarrow N'$ innjective. I want to show that $f \otimes Id$ is injective.