Let the system of equations be $a_{1} x + b_{1} y + c_{1} z = d_{1}, a_{2} x + b_{2} y + c_{2} z = d_{2}$ and $a_{3} x + b_{3} y + c_{3} z = d_{3} .$
$S_{1} :$ If $D = 0$ and $D_{1} = D_{2} = D_{3} = 0,$ then the system is consistent, with infinitely many solutions.
$S_{2} :$ If $D = 0$ and $D_{1} = D_{2} = D_{3} = 0,$ then the system is inconsistent
$S_{3} :$ If $D \neq 0$ and $D_{1} = D_{2} = D_{3} = 0,$ then the system has only trivial solution $(x = y = z = 0)$
Then, the number of statements which are true is

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answer is D.

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$A X = B$ is consistent when $| A | \neq 0$ and has unique solution.

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