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CUET · MATHS · PYQ PAPER 2023

If \(A, B\) are symmetric matrices of the same order, then \(A B-B A\) is a :

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

Answer & Solution

Correct Answer

(A) Skew-symmetric matrix

Step-by-step Solution

Detailed explanation

\((AB-BA)^T = (AB)^T - (BA)^T\) \(= B^T A^T - A^T B^T\) Since \(A^T=A\) and \(B^T=B\), \(= BA - AB\) \(= -(AB - BA)\) Therefore, \(AB-BA\) is a skew-symmetric matrix.