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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Matrices

NDA 2023 · Mathematics · Matrices

If A=[ array ccc 2 & -1 & 0 -1 & 3 & 0 1 & 0 & 1 array ] , then...

If A=\left[2−10−130101\begin{array}{ccc}2 & -1 & 0 \\ -1 & 3 & 0 \\ 1 & 0 & 1\end{array}\right], then what is the value of det⁡⁡[adj⁡(adj⁡A)]?\operatorname\det[\operatorname{adj}(\operatorname{adj} A)] ?

Options

  1. A5
  2. B25
  3. C125
  4. D625

Correct answer

D. 625

Step-by-step solution

Since, ∣A∣=1(6−1)=5|A|=1(6-1)=5 Now, ∣adj⁡(adj⁡A)∣=∣A∣(n−1)2=5(3−1)2=54=625|\operatorname{adj}(\operatorname{adj} A)|=|\mathrm{A}|^{(\mathrm{n}-1)^2}=5^{(3-1)^2}=5^4=625
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