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Let A and B be two 3 × 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)
    adj (A) is an invertible matrix
Correct answer is option 'B'. Can you explain this answer?
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Let A and B be two 3 × 3 non-zero real matrices such that AB is ...
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Let A and B be two 3 × 3 non-zero real matrices such that AB is ...
AB = 0
⇒ |AB| = 0

If |A| 
≠ 
0, B = 0 (not possible)
If |B| 
 0, A = 0 (not possible)
Hence, |A| = |B| = 0
 AX = 0 has infinitely many solutions.
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Let A and B be two 3 × 3 non-zero real matrices such that AB is a zero matrix. Thena)the system of linear equations AX = 0 has a unique solutionb)the system of linear equations AX = 0 has infinitely many solutionsc)B is an invertible matrixd)adj (A) is an invertible matrixCorrect answer is option 'B'. Can you explain this answer?
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Let A and B be two 3 × 3 non-zero real matrices such that AB is a zero matrix. Thena)the system of linear equations AX = 0 has a unique solutionb)the system of linear equations AX = 0 has infinitely many solutionsc)B is an invertible matrixd)adj (A) is an invertible matrixCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let A and B be two 3 × 3 non-zero real matrices such that AB is a zero matrix. Thena)the system of linear equations AX = 0 has a unique solutionb)the system of linear equations AX = 0 has infinitely many solutionsc)B is an invertible matrixd)adj (A) is an invertible matrixCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let A and B be two 3 × 3 non-zero real matrices such that AB is a zero matrix. Thena)the system of linear equations AX = 0 has a unique solutionb)the system of linear equations AX = 0 has infinitely many solutionsc)B is an invertible matrixd)adj (A) is an invertible matrixCorrect answer is option 'B'. Can you explain this answer?.
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