It's a bird! It's a plane! It's not superman...

A system of three linear equations with three variables $x, y, z$ in the form

$\left\{\begin{matrix} ax+by+cz = d\\ ex+fy+gz = h \\ ix+jy+kz = l \end{matrix}\right.$

with $(a, b, c, d, e, f, g, h, i, j, k, l) \in \mathbb{Z}$ could be considered geometrically as three different planes intersecting each other in various ways, depending what those coefficients are. Some of the coefficients may be equal to other coefficients--or not.

Let $\text{A}$ be the coefficient matrix of that above system. If $\text{det(A)} = 0$ , which of the following could be true about the system?

A. The planes are all parallel to each other.

B. A line is formed by the intersection of all three planes.

C. The planes form a triangular prism missing the triangular faces.

D. The planes all intersect at a single point.