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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Matrices

NDA 2013 · Mathematics · Matrices

If A is a square matrix of order 3 with |A| ≠ 0 , then which one of...

If AA is a square matrix of order 3 with ∣A∣≠0|\mathrm{A}| \neq 0, then which one of the following is correct?

Options

  1. A∣adj⁡A∣=∣A∣|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|
  2. B∣adj⁡A∣=∣A∣2|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^2
  3. C∣adj⁡A∣=∣A∣3|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^3
  4. D∣adj⁡A∣2=∣A∣|\operatorname{adj} A|^2=|\mathrm{A}|

Correct answer

B. ∣adj⁡A∣=∣A∣2|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^2

Step-by-step solution

As ∣A∣≠0|\mathrm{A}| \neq 0, It is non-singular matrix. Hence, ∣Adj⁡A∣=∣A∣2|\operatorname{Adj} \mathrm{A}|=|\mathrm{A}|^2
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