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If A and B are two matrices conformable to multiplication such that their product AB = O(Zero matrix). Then which of the following can be true
- a)A and B are both null matrices
- b)Either of A is or B is a null matrix
- c)Either of them may be a zero matrix
- d)It is Not necessary that A = 0 or B = 0
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If A and B are two matrices conformable to multiplication such that th...
AB = 0 does not necessarily imply that either A or B is a null matrix
- Both matrices need not be null matrices.
- Both matrices need not be null matrices.
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If A and B are two matrices conformable to multiplication such that th...
Explanation:
When two matrices A and B are multiplied, the resulting matrix will have the same number of rows as A and the same number of columns as B. If the product of two matrices AB is a zero matrix, then it means that all the entries of the resulting matrix are zero. This condition implies that the product of any row of A with any column of B results in zero.
Possible Cases:
1. A and B are both null matrices:
If both matrices A and B are null matrices, then their product AB will also be a null matrix. This condition satisfies the given statement. Hence, option A is correct.
2. Either of A is or B is a null matrix:
If either matrix A or B is a null matrix, then their product AB will also be a null matrix. This is because the product of any non-zero matrix with a null matrix results in a null matrix. Hence, option B is correct.
3. Neither of them may be a zero matrix:
It is possible that neither matrix A nor B is a null matrix, but their product AB is still a null matrix. For example, consider the matrices A = [1 0] and B = [0 0; 0 0]. Their product AB = [0 0; 0 0] is a null matrix. Hence, option C is not always correct.
Conclusion:
From the above analysis, we can conclude that options A, B, and C are not mutually exclusive. Hence, option D, i.e., all of the above options are correct, is the correct answer.
When two matrices A and B are multiplied, the resulting matrix will have the same number of rows as A and the same number of columns as B. If the product of two matrices AB is a zero matrix, then it means that all the entries of the resulting matrix are zero. This condition implies that the product of any row of A with any column of B results in zero.
Possible Cases:
1. A and B are both null matrices:
If both matrices A and B are null matrices, then their product AB will also be a null matrix. This condition satisfies the given statement. Hence, option A is correct.
2. Either of A is or B is a null matrix:
If either matrix A or B is a null matrix, then their product AB will also be a null matrix. This is because the product of any non-zero matrix with a null matrix results in a null matrix. Hence, option B is correct.
3. Neither of them may be a zero matrix:
It is possible that neither matrix A nor B is a null matrix, but their product AB is still a null matrix. For example, consider the matrices A = [1 0] and B = [0 0; 0 0]. Their product AB = [0 0; 0 0] is a null matrix. Hence, option C is not always correct.
Conclusion:
From the above analysis, we can conclude that options A, B, and C are not mutually exclusive. Hence, option D, i.e., all of the above options are correct, is the correct answer.
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If A and B are two matrices conformable to multiplication such that their product AB = O(Zero matrix). Then which of the following can be truea)A and B are both null matricesb)Either of A is or B is a null matrixc)Either of them may be a zero matrixd)It is Not necessary that A = 0 or B = 0Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If A and B are two matrices conformable to multiplication such that their product AB = O(Zero matrix). Then which of the following can be truea)A and B are both null matricesb)Either of A is or B is a null matrixc)Either of them may be a zero matrixd)It is Not necessary that A = 0 or B = 0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are two matrices conformable to multiplication such that their product AB = O(Zero matrix). Then which of the following can be truea)A and B are both null matricesb)Either of A is or B is a null matrixc)Either of them may be a zero matrixd)It is Not necessary that A = 0 or B = 0Correct answer is option 'D'. Can you explain this answer?.
If A and B are two matrices conformable to multiplication such that their product AB = O(Zero matrix). Then which of the following can be truea)A and B are both null matricesb)Either of A is or B is a null matrixc)Either of them may be a zero matrixd)It is Not necessary that A = 0 or B = 0Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If A and B are two matrices conformable to multiplication such that their product AB = O(Zero matrix). Then which of the following can be truea)A and B are both null matricesb)Either of A is or B is a null matrixc)Either of them may be a zero matrixd)It is Not necessary that A = 0 or B = 0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are two matrices conformable to multiplication such that their product AB = O(Zero matrix). Then which of the following can be truea)A and B are both null matricesb)Either of A is or B is a null matrixc)Either of them may be a zero matrixd)It is Not necessary that A = 0 or B = 0Correct answer is option 'D'. Can you explain this answer?.
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