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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Determinants

NDA 2023 · Mathematics · Determinants

The value of the determinant of a matrix A of order 3 is 3. If C is...

The value of the determinant of a matrix AA of order 3 is 3. If C is the matrix of cofactors of the matrix A , then what is the value of determinant of C2\mathrm{C}^2 ?

Options

  1. A3
  2. B9
  3. C81
  4. D729

Correct answer

C. 81

Step-by-step solution

Given ∣A∣=3,(∴whereA3×3)Since,|A|=3, \left(\therefore\right. where \left.\mathrm{A}_{3 \times 3}\right) Since,C=(\operatorname{adj}(A))^{\prime}Now,Now,|C∣=∣adj⁡A∣=∣A∣n−1=\mathrm{C}|=|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^{\mathrm{n}-1}=3^2=9So, \left|C^2\right|=9^2=81
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