CUET · MATHS · PYQ PAPER 2025
Which of the following statement(s) is/are TRUE?
(A) Skew symmetric matrix of even order is always symmetric
(B) Skew symmetric matrix of odd order is non-singular
(C) Skew symmetric matrix of odd order is singular
(D) Skew symmetric matrix is always square matrix
Choose the correct answer from the options given below:
- A (A) and (D) only
- B (C) and (D) only
- C (B) and (D) only
- D (A) and (C) only
Answer & Solution
Correct Answer
(B) (C) and (D) only
Step-by-step Solution
Detailed explanation
\( \det(A) = (-1)^n \det(A) \). For odd \( n \), \( \det(A) = -\det(A) \Rightarrow \det(A) = 0 \). Statement (C) is TRUE. Skew symmetric matrix definition \( A^T = -A \) implies A must be square. Statement (D) is TRUE. (C) and (D) only
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