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CUET · MATHS · PYQ PAPER 2023

If \(A\) and \(B\) are square matrices of the same order, then \(A B^T-B A^T\) is a

  1. A Symmetric matrix
  2. B Skew symmetric matrix
  3. C Identity matrix
  4. D Zero matrix
Verified Solution

Answer & Solution

Correct Answer

(B) Skew symmetric matrix

Step-by-step Solution

Detailed explanation

Let \(C = A B^T - B A^T\). \(C^T = (A B^T - B A^T)^T\) \(C^T = (A B^T)^T - (B A^T)^T\) \(C^T = (B^T)^T A^T - (A^T)^T B^T\) \(C^T = B A^T - A B^T\) \(C^T = -(A B^T - B A^T)\) \(C^T = -C\) Thus, \(A B^T - B A^T\) is a skew symmetric matrix.