Let $AX = B$ be a system of three linear equations in three variables. Then the system has

(A) a unique solutions if $|A| = 0$
(B) a unique solutions if |$A| ≠ 0$
(C) no solutions if $|A| = 0$ and $(adj\, A)B ≠0$
(D) infinitely many solutions if $|A| = 0$ and $(adj\, A)B = 0$

Choose the correct answer from the options given below:

(B), (C) and (D) only

The correct answer is Option (2) → (B), (C) and (D) only

(B), (C) and (D) are correct.

Reason:

If $|A|\neq 0$, the system $AX=B$ has a unique solution.

If $|A|=0$ and $(adj\,A)B\neq 0$, the system has no solution.

If $|A|=0$ and $(adj\,A)B=0$, the system has infinitely many solutions.