For the system of linear equations: \[x-2 y=1, x-y+k z=-2, k y+4 z=6, k \in R \text {, }\] Consider the following statem…

For the system of linear equations: \[x-2 y=1, x-y+k z=-2, k y+4 z=6, k \in R \text {, }\] Consider the following statements:
(A) The system has unique solution if \(k \neq 2, k \neq-2\).
(B) The system has unique solution if \(k=-2\).
(C) The system has unique solution if \(k=2\).
(D) The system has no solution if \(k=2\).
(E) The system has infinite number of solutions if \(k \neq-2\). Which of the following statements are correct?

[JEE Main 2021, 24 Feb (Shift 2)]