When is $\left\{\begin{pmatrix} x & yb \\ y & x \\ \end{pmatrix} : x,y\in \mathbb{Q}\right\}$ an integral domain?

Question

Any hint about this exercise I am struggling with?

Let $b \in \mathbb{Z}$ and

$$A=\left\{ \begin{pmatrix} x & yb \\ y & x \\ \end{pmatrix} : x,y\in \mathbb{Q}\right\}.$$ Now, $A$ is a commutative sub-ring of $M(2,\mathbb{Q})$, prove that $A$ is an integral domain $\iff$ $b$ is not a square in $\mathbb{Z}$