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CUET · MATHS · PYQ PAPER 2025

If \(A\) and \(B\) are symmetric matrices of order \(3 \times 3\) then the matrix \(2 A B-B A\) is :

  1. A a symmetric matrix
  2. B a skew-symmetric matrix
  3. C both symmetric and skew-symmetric matrix
  4. D neither symmetric nor skew-symmetric matrix
Verified Solution

Answer & Solution

Correct Answer

(D) neither symmetric nor skew-symmetric matrix

Step-by-step Solution

Detailed explanation

\(X = 2AB - BA\) \(X^T = (2AB - BA)^T\) \(X^T = 2(AB)^T - (BA)^T\) \(X^T = 2B^T A^T - A^T B^T\) Given \(A^T = A\) and \(B^T = B\): \(X^T = 2BA - AB\) Since \(X^T \neq X\) and \(X^T \neq -X\) in general, the matrix is neither symmetric nor skew-symmetric.