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CUET · MATHS · PYQ PAPER 2025

If \(A\) and \(B\) are matrices of same order, then ( \(A B^{ T }-B A^{ T }\) ) is always:

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

Answer & Solution

Correct Answer

(B) a skew symmetric matrix

Step-by-step Solution

Detailed explanation

Let \( C = A B^{ T }-B A^{ T } \). \( C^{ T } = (A B^{ T }-B A^{ T})^{ T } \) \( C^{ T } = (A B^{ T})^{ T } - (B A^{ T})^{ T } \) \( C^{ T } = (B^{ T})^{ T } A^{ T } - (A^{ T})^{ T } B^{ T } \) \( C^{ T } = B A^{ T } - A B^{ T } \) \( C^{ T } = - (A B^{ T } - B A^{ T}) \)…