Matrices And Determinants

Let $I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$ and $P=\left(\begin{array}{ll}2 & 0 \\ 0 & 3\end{array}\right)$. Let $Q=\left(\begin{array}{ll}x & y \\ z & 4\end{array}\right)$ for some non-zero real numbers $x, y$, and $z$, for which there is a $2 \times 2$ matrix $R$ with all entries being non-zero real numbers, such that $Q R=R P$.

Then which of the following statements is (are) TRUE?