JEE Math Practice Question

For the system of linear equations $$\alpha x+y+z=1,x+\alpha y+z=1,x+y+\alpha z=\beta$$, which one of the following statements is NOT correct?

1. A.It has infinitely many solutions if $$\alpha=1$$ and $$\beta=1$$
2. B.It has infinitely many solutions if $$\alpha=2$$ and $$\beta=-1$$
3. C.$$x+y+z=\frac{3}{4}$$ if $$\alpha=2$$ and $$\beta=1$$
4. D.It has no solution if $$\alpha=-2$$ and $$\beta=1$$