JEE Math Practice Question

Consider the system of linear equations $$x+y+z=5, x+2 y+\lambda^2 z=9, x+3 y+\lambda z=\mu$$, where $$\lambda, \mu \in \mathbb{R}$$. Then, which of the following statement is NOT correct?

1. A.System is consistent if $$\lambda \neq 1$$ and $$\mu=13$$
2. B.System is inconsistent if $$\lambda=1$$ and $$\mu \neq 13$$
3. C.System has unique solution if $$\lambda \neq 1$$ and $$\mu \neq 13$$
4. D.System has infinite number of solutions if $$\lambda=1$$ and $$\mu=13$$