Exercise 4, § 3

Let $E$ be a right $A$-module and $F$ a free left $A$-module. Show that if $x$ is a free element of $E$ and $y$ an element $\neq 0$ of $F$, then $x \otimes y \neq 0$; if also $A$ is commutative and $y$ is a free element of $F$, then $x \otimes y$ is free in the $A$-module $E \otimes_A F$.