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
- A Symmetric matrix
- B Skew symmetric matrix
- C Identity matrix
- D Zero matrix
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.
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