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Let A and B be two symmetric matrices of...

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-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.    Statement-1 is true, Statement-2 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.    Statement-1 is true, Statement-2 is false.    Statement-1 is false, Statement-2 is true.

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To solve the problem, we need to analyze the two statements regarding the symmetric matrices \( A \) and \( B \). ### Step 1: Understanding Symmetric Matrices A matrix \( M \) is symmetric if \( M^T = M \). Given that both \( A \) and \( B \) are symmetric matrices, we have: - \( A^T = A \) - \( B^T = B \) ### Step 2: Checking Statement 1 ...
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Knowledge Check

  • Let A and B 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 false, statement 2 is true.
    B
    Statement 1 is true, statement 2 is true, statement 2 is a correct explanation for statement 1.
    C
    Statement 1 is true, statement 2 is true, statement 2 is not a correct explanation for statement 1.
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  • Let A and B are 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
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    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
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