Consider the following system of equations
$$\alpha x + 2y + z = 1$$
$$2\alpha x + 3y + z = 1$$
$$3x + \alpha y + 2z = \beta$$
For some $$\alpha, \beta \in \mathbb{R}$$. Then which of the following is NOT correct.

A

It has no solution if $$\alpha = -1$$ and $$\beta \neq 2$$

B

It has no solution for $$\alpha = -1$$ and for all $$\beta \in \mathbb{R}$$

C

It has no solution for $$\alpha = 3$$ and for all $$\beta \neq 2$$

D

It has a solution for all $$\alpha \neq -1$$ and $$\beta = 2$$