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Let A and B be two symmetric matrices of order 3.
Statement-1: A(BA) and (AB)A are symmetric matrices.
Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.
Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.
- a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- b)Statement-1 is true, Statement-2 is false.
- c)Statement-1 is false, Statement-2 is true.
- d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Let A and B be two symmetric matrices of order 3.Statement-1: A(BA) an...
Explanation:
Statement-1: A(BA) and (AB)A are symmetric matrices.
Let C = AB. Then, (AB)A = CAB and A(BA) = CBA. Now, we have to prove that C^T = C.
Since A and B are symmetric matrices, we have:
A^T = A and B^T = B
Now, we can write:
C^T = (AB)^T = B^T A^T = BA = C
Therefore, C^T = C, which implies that (AB)A and A(BA) are symmetric matrices.
Statement-2: AB is a symmetric matrix if matrix multiplication of A with B is commutative.
If AB is a symmetric matrix then AB = (AB)^T = B^T A^T = BA. Hence, the matrix multiplication of A with B is commutative. However, the converse is not true. That is, just because A and B commute, it does not necessarily imply that AB is symmetric.
Option A: Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
From the above explanation, we can see that both statements are true. However, Statement-2 does not explain why Statement-1 is true. Therefore, option A is the correct answer.
Statement-1: A(BA) and (AB)A are symmetric matrices.
Let C = AB. Then, (AB)A = CAB and A(BA) = CBA. Now, we have to prove that C^T = C.
Since A and B are symmetric matrices, we have:
A^T = A and B^T = B
Now, we can write:
C^T = (AB)^T = B^T A^T = BA = C
Therefore, C^T = C, which implies that (AB)A and A(BA) are symmetric matrices.
Statement-2: AB is a symmetric matrix if matrix multiplication of A with B is commutative.
If AB is a symmetric matrix then AB = (AB)^T = B^T A^T = BA. Hence, the matrix multiplication of A with B is commutative. However, the converse is not true. That is, just because A and B commute, it does not necessarily imply that AB is symmetric.
Option A: Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
From the above explanation, we can see that both statements are true. However, Statement-2 does not explain why Statement-1 is true. Therefore, option A is the correct answer.
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Let A and B be two symmetric matrices of order 3.Statement-1: A(BA) an...
Option A is correct as, 1st statement tells about associativity and 2nd statement tells about commutativity . but finay both are true statements.
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Let A and B be two symmetric matrices of order 3.Statement-1: A(BA) and (AB)A are symmetric matrices.Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'A'. Can you explain this answer?
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Let A and B be two symmetric matrices of order 3.Statement-1: A(BA) and (AB)A are symmetric matrices.Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'A'. 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 symmetric matrices of order 3.Statement-1: A(BA) and (AB)A are symmetric matrices.Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'A'. 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 symmetric matrices of order 3.Statement-1: A(BA) and (AB)A are symmetric matrices.Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'A'. Can you explain this answer?.
Let A and B be two symmetric matrices of order 3.Statement-1: A(BA) and (AB)A are symmetric matrices.Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'A'. 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 symmetric matrices of order 3.Statement-1: A(BA) and (AB)A are symmetric matrices.Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'A'. 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 symmetric matrices of order 3.Statement-1: A(BA) and (AB)A are symmetric matrices.Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'A'. Can you explain this answer?.
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ample number of questions to practice Let A and B be two symmetric matrices of order 3.Statement-1: A(BA) and (AB)A are symmetric matrices.Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
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