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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

  1. A \(\frac{15}{212}\)
  2. B 60
  3. C \(\frac{212}{15}\)
  4. D \(\frac{1}{60}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{1}{60}\)

Step-by-step Solution

Detailed explanation

\(|A| = 9 \times 16 \times 25 = 3600\) \(|B| = \frac{1}{5} \times \frac{1}{4} \times \frac{1}{3} = \frac{1}{60}\) \(|AB| = |A||B| = 3600 \times \frac{1}{60} = 60\) \(|(AB)^{-1}| = \frac{1}{|AB|} = \frac{1}{60}\)