CUET · MATHS · PYQ PAPER 2025
If \(A=\left[\begin{array}{lll}1 & 2 & 1 \\ 2 & 3 & 1 \\ 0 & 0 & 1\end{array}\right]\), then \(\left|\operatorname{adj}\left(3 A^T\right)\right|^2\) is equal to
- A \(3^6\)
- B \(3^9\)
- C \(3^{12}\)
- D \(3^{18}\)
Answer & Solution
Correct Answer
(C) \(3^{12}\)
Step-by-step Solution
Detailed explanation
\(|A| = 1(3 \cdot 1 - 1 \cdot 0) - 2(2 \cdot 1 - 1 \cdot 0) + 1(2 \cdot 0 - 3 \cdot 0) = 3 - 4 + 0 = -1\) \(|\operatorname{adj}(3 A^T)| = |3 A^T|^{3-1} = |3 A^T|^2\) \(|3 A^T| = 3^3 |A^T| = 3^3 |A| = 27(-1) = -27\) \(|\operatorname{adj}(3 A^T)| = (-27)^2 = (-(3^3))^2 = 3^6\)…
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