AP EAMCET · Maths · Matrices
If the determinant of a \(3^{\text {rd }}\) order matrix A is K , then the sum of the determinants of the matrices \(\left(A A^T\right)\) and \(\left(A-A^T\right)\) is
- A \(\mathrm{2K}\)
- B \(0\)
- C \(\mathrm{K}^2\)
- D \(\mathrm{K}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{K}^2\)
Step-by-step Solution
Detailed explanation
Given, A is \(3 \times 3\) matrix and \(|\mathrm{A}|=\mathrm{k}\) Now, \(\mathrm{A}-\mathrm{A}^{\mathrm{T}}\) is always a skew symmetric matrix of order 3 So, \(\left|\mathrm{A}-\mathrm{A}^{\mathrm{T}}\right|=0\) and…
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