Intersection 3 planes is a single point, then the triple scalar is non-zero?

Question

I know that, if the triple scalar product between the normal vectors of three planes is non-zero, then they intercept in a single-point.

May I affirm that if the intersection is a single point, hence the triple scalar product of their normal vectors is non-zero?

Answer 1

The condition reduces to

• $Ax = b$ has exactly one solution $\iff$ matrix $A$ is full rank

which is true by Rouché–Capelli theorem.