CUET · MATHS · PYQ PAPER 2023
If \(A, B\) are symmetric matrices of the same order, then \(A B-B A\) is a :
- A Skew-symmetric matrix
- B Symmetric matrix
- C Zero matrix
- D Identity matrix
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.
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