Let $\alpha$, $\beta$ and $\gamma$ be real numbers such that the system of linear equations $$x + 2y + 3z = \alpha$$ $$4x + 5y + 6z = \beta$$ $$7x + 8y + 9z = \gamma - 1$$ is consistent. Let $|M|$ represent the determinant of the matrix $$M = \begin{pmatrix} \alpha & 1 & 0 \\ \beta & 2 & 1 \\ \gamma & 1 & 0 \end{pmatrix}.$$ Let $P$ be the plane containing all those $(\alpha, \beta, \gamma)$ for which the above system of linear equations is consistent, and $D$ be the square of the distance of the point $(0, 1, 0)$ from the plane $P$. The value of $|M|$ is ____.
Let $\alpha$, $\beta$ and $\gamma$ be real numbers such that the system of linear equations
$$x + 2y + 3z = \alpha$$
$$4x + 5y + 6z = \beta$$
$$7x + 8y + 9z = \gamma - 1$$
is consistent. Let $|M|$ represent the determinant of the matrix
$$M = \begin{pmatrix} \alpha & 1 & 0 \\ \beta & 2 & 1 \\ \gamma & 1 & 0 \end{pmatrix}.$$
Let $P$ be the plane containing all those $(\alpha, \beta, \gamma)$ for which the above system of linear equations is consistent, and $D$ be the square of the distance of the point $(0, 1, 0)$ from the plane $P$.
The value of $|M|$ is ____.