JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) and \(B\) be two \(3 \times 3\) non-zero real matrices such that \(AB\) is a zero matrix. Then.
- A The system of linear equations \(AX =0\) has a unique solution
- B The system of linear equations \(AX =0\) has infinitely many solutions
- C \(B\) is an invertible matrix
- D \(\operatorname{adj}\) \((A)\) is an invertible matrix
Answer & Solution
Correct Answer
(B) The system of linear equations \(AX =0\) has infinitely many solutions
Step-by-step Solution
Detailed explanation
\(AB =0 \Rightarrow| AB |=0\) If \(| A | \neq 0, B =0\) (not possible) If \(| B | \neq 0, A =0\) (not possible) Hence \(| A |=| B |=0\) \(AX =0\) has infinitely many solutions
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