CUET · MATHS · PYQ PAPER 2025
If A is a skew-symmetric matrix, then which of the following statements is NOT true?
(A) A is singular if order of A is odd
(B) A is non-singular
(C) \(A^{2025}\) is a skew-symmetric matrix
(D) \(A^{2025}\) is a symmetric matrix
(E) all diagonal elements of A are zeros
Choose the correct answer from the option given below :
- A (A), (C) and (E) only
- B (A) and (E) only
- C (B), (D) and (E) only
- D (B) and (D) only
Answer & Solution
Correct Answer
(D) (B) and (D) only
Step-by-step Solution
Detailed explanation
(B) If A is skew-symmetric and order is odd, then \(det(A) = 0\). Thus A is singular. Statement (B) is NOT true. (D) \((A^{2025})^T = (A^T)^{2025} = (-A)^{2025} = -A^{2025}\). Thus \(A^{2025}\) is skew-symmetric. Statement (D) is NOT true. The statements (B) and (D) are NOT true.
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