CUET · MATHS · PYQ PAPER 2025
Consider the matrices \(A=\left[\begin{array}{ccc}9 & 0 & 0 \\ 0 & 16 & 0 \\ 0 & 0 & 25\end{array}\right]\) and \(B=\left[\begin{array}{ccc}1 / 5 & 0 & 0 \\ 0 & 1 / 4 & 0 \\ 0 & 0 & 1 / 3\end{array}\right]\). The value of \(\left|(A B)^{-1}\right|\) is
- A \(\frac{15}{212}\)
- B 60
- C \(\frac{212}{15}\)
- D \(\frac{1}{60}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{60}\)
Step-by-step Solution
Detailed explanation
\(|A| = 9 \times 16 \times 25 = 3600\) \(|B| = \frac{1}{5} \times \frac{1}{4} \times \frac{1}{3} = \frac{1}{60}\) \(|AB| = |A||B| = 3600 \times \frac{1}{60} = 60\) \(|(AB)^{-1}| = \frac{1}{|AB|} = \frac{1}{60}\)
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