TS EAMCET · Maths · Matrices
Let \(A\) and \(B\) be two symmetric matrices of same order. Then, the matrix \(A B-B A\) is
- A a symmetric matrix
- B a skew-symmetric matrix
- C a null matrix
- D the identity matrix
Answer & Solution
Correct Answer
(B) a skew-symmetric matrix
Step-by-step Solution
Detailed explanation
Given, \(A=A^{\prime}, B=B^{\prime}\) Now, \((A B-B A)^{\prime}=(A B)^{\prime}-(B A)^{\prime}\) \(\begin{aligned} & =B^{\prime} A^{\prime}-A^{\prime} B^{\prime} \\ & =B A-A B \\ & =-(A B-B A) \end{aligned}\) \(\therefore A B-B A\) is a skew-symmetric matrix.
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