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JEE Advance | PYQ

Let \(\displaystyle I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \text{ and } P = \begin{pmatrix} 2 & 0 \\ 0 & 3 \end{pmatrix}. \text{ Let } Q = \begin{pmatrix} x & y \\ z & 4 \end{pmatrix}\)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?

Consider the matrix \(\displaystyle P = \begin{pmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{pmatrix}\).
Let the transpose of a matrix \( X \) be denoted by \( X^T \). Then the number of \( 3\times 3 \) invertible matrices \( Q \) with integer entries, such that \( Q^{-1}=Q^T \) and \( PQ=QP \) is: