Proposition 2

Let $E$ be a faithfully flat right $A$-module and $u : N' \to N$ a left $A$-module homomorphism. For $u$ to be injective (resp. surjective, bijective), it is necessary and sufficient that $1_E \otimes u : E \otimes_A N' \to E \otimes_A N$ be so.

This is an immediate consequence of criterion (a) of Proposition 1.