AP EAMCET · Maths · Matrices
If \(A\) and \(B\) are square matrices of order 3 , then \(\left|\left(A-A^T\right)+\left(B-B^T\right)\right|=\)
- A \(2|\mathrm{~A}|\)
- B \(2|\mathrm{~B}|\)
- C \(2(|\mathrm{~A}|+|\mathrm{B}|)\)
- D \(0\)
Answer & Solution
Correct Answer
(D) \(0\)
Step-by-step Solution
Detailed explanation
Let \\(M = (A-A^T) + (B-B^T)\\). Since \\(A\\) and \\(B\\) are square matrices of order 3, \\(A-A^T\\) and \\(B-B^T\\) are skew-symmetric matrices of order 3. The sum of two skew-symmetric matrices is a skew-symmetric matrix: \…
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