Let $I = \left( \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right)$ and $P = \left( \begin{array} { l l } 2 & 0 \\ 0 & 3 \end{array} \right)$. Let $Q = \left( \begin{array} { l l } x & y \\ z & 4 \end{array} \right)$ 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?

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\begin{tabular}{ | l | l | }
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(A) & The determinant of $Q - 2 I$ is zero \\
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(B) & The determinant of $Q - 6 I$ is 12 \\
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(C) & The determinant of $Q - 3 I$ is 15 \\
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(D) & $y z = 2$ \\
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\end{tabular}
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