CUET · MATHS · PYQ PAPER 2025
Let \(A\) be a matrix such that \(A=\left[\begin{array}{cc}1 & 2 \\ -2 & 3\end{array}\right]\) Then which of the following are TRUE?
(A) \(A\) is a non-singular matrix
(B) \(A^T=A\)
(C) \(A\) is not an invertible matrix
(D) \(A\) is not a skew-symmetric matrix
Choose the correct answer from the options given below :
- A (A) and (D) only
- B (B) and (C) only
- C (A) and (C) only
- D (C) and (D) only
Answer & Solution
Correct Answer
(A) (A) and (D) only
Step-by-step Solution
Detailed explanation
\( \det(A) = (1)(3) - (2)(-2) = 7 \) Since \( \det(A) \neq 0 \), (A) is TRUE (non-singular) and (C) is FALSE (invertible). \( A^T = \left[\begin{array}{cc}1 & -2 \\ 2 & 3\end{array}\right] \) Since \( A^T \neq A \), (B) is FALSE. Since \( A^T \neq -A \), (D) is TRUE. The correct…
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