Let $\alpha$ and $\beta$ be the distinct roots of the equation $x^2+x-1=0$. Consider the set $T=\{1, \alpha, \beta\}$. For a $3 \times 3$ matrix $M=\left(a_{i j}\right)_{3 \times 3}$, define $R_i=a_{i 1}+a_{i 2}+a_{i 3}$ and $C_j=a_{1 j}+a_{2 j}+a_{3 j}$ for $i=1,2,3$ and $j=1,2,3$.

Match each entry in List-I to the correct entry in List-II.

List-I	List-II
(P) The number of matrices $M = (a_{ij})_{3x3}$ with all entries in $T$ such that $R_i = C_j = 0$ for all $i, j$, is	(1) 1
(Q) The number of symmetric matrices $M = (a_{ij})_{3x3}$ with all entries in $T$ such that $C_j = 0$ for all $j$, is	(2) 12
(R) Let $M = (a_{ij})_{3x3}$ be a skew symmetric matrix such that $a_{ij} \in T$ for $i \gt j$. Then the number of elements in the set $\left\{ \begin{pmatrix} x \\ y \\ z \end{pmatrix} : x, y, z \in \mathbb{R}, M \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} a_{12} \\ 0 \\ a_{13} \end{pmatrix} \right\}$ is	(3) infinite
(S) Let $M = (a_{ij})_{3x3}$ be a matrix with all entries in $T$ such that $R_i = 0$ for all $i$. Then the absolute value of the determinant of $M$ is	(4) 6

The correct option is