AP EAMCET · Maths · Matrices
If \(A\) is a Skew-symmetric matrix then (given \(n \in \mathbf{N}\))
1. \(A^{2 n}\) is Skew-symmetric matrix.
2. \(A^{2 n+1}\) is Skew-symmetric matrix.
- A 1 is true, 2 is false
- B Both 1 and 2 are true
- C Both 1 and 2 are false
- D 1 is false, 2 is true
Answer & Solution
Correct Answer
(D) 1 is false, 2 is true
Step-by-step Solution
Detailed explanation
Given, \(A\) is a skew symmetric matrix \(\begin{aligned} \therefore \quad A^T & =-A \Rightarrow\left(A^{2 n}\right)^T=\left(A^T\right)^{2 n}=(-A)^{2 n} \\ \left(A^{2 n}\right)^T & =A^{2 n} \end{aligned}\) \(\therefore A^{2 n}\) is Symmetric Matrix…
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