CUET · MATHS · PYQ PAPER 2025
If \(A\) is a \(3 \times 3\) matrix such that \(|\operatorname{adj} A|=9\) and \(\left|k A^{-1}\right|=9\), then the value of \(k\) are :
- A \(\pm 1\)
- B \(\pm \frac{1}{3}\)
- C \(\pm 3\)
- D \(\pm \frac{1}{9}\)
Answer & Solution
Correct Answer
(C) \(\pm 3\)
Step-by-step Solution
Detailed explanation
\(|\operatorname{adj} A|=|A|^{n-1}\) \(9 = |A|^{3-1}\) \(9 = |A|^2 \implies |A|=\pm 3\) \(|k A^{-1}| = k^n |A^{-1}| = k^n \frac{1}{|A|}\) \(9 = k^3 \frac{1}{\pm 3}\) \(k^3 = 9 (\pm 3)\) \(k^3 = \pm 27\) \(k = \pm 3\)
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