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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Matrices

NDA 2010 · Mathematics · Matrices

If |A|=8 , where A is a square matrix of order 3 , then what is...

If ∣A∣=8|\mathrm{A}|=8, where AA is a square matrix of order 3 , then what is ∣adj⁡A∣|\operatorname{adj} A| equal to ?

Options

  1. A16
  2. B24
  3. C64
  4. D512

Correct answer

C. 64

Step-by-step solution

 Since ∣A∣=8≠0∴∣adj⁡A∣=∣A∣n−1\begin{aligned} & \text{ Since }|\mathrm{A}|=8 \neq 0 \\ & \therefore|\operatorname{adj} \mathrm{ A}|=|\mathrm{A}|^{n-1} \end{aligned} where nn is order of the matrix ∴∣adj⁡A∣=∣8∣3−1=∣8∣2=64.\therefore|\operatorname{adj} \mathrm{A}|=|^{8}|^{3-1}=|^{8}|^2=64 .
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