Matrices and Determinants: JEE Main 2024 Mathematics question

Let for any three distinct consecutive terms $a, b, c$ of an A.P, the lines $a x+b y+c=0$ be concurrent at the point $P$ and $Q(\alpha, \beta)$ be a point such that the system of equations $\begin{aligned} & x+y+z=6, \\ & 2 x+5 y+\alpha z=\beta \text { and } \end{aligned}$ $x+2 y+3 z=4$, has infinitely many solutions. Then $(P Q)^2$ is equal to _________.