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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Matrices

NDA 2020 · Mathematics · Matrices

Consider the following in respect of a non-singular matrix of order...

Consider the following in respect of a non-singular matrix of order 3 : 1. A(adj⁡A)=(adj⁡A)A2.\quad \mathrm{A}(\operatorname{adj} \mathrm{A})=(\operatorname{adj} \mathrm{A}) \mathrm{A} 2.|adj⁡A\operatorname{adj} \mathrm{A}|=|A\mathrm{A}|Whichoftheabovestatementsis/arecorrect?Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

A. 1 only

Step-by-step solution

(1) We know that, A⋅(adj⁡A)=(adj⁡A)⋅A=∣A∣⋅IA \cdot(\operatorname{adj} A)=(\operatorname{adj} A) \cdot A=|A| \cdot I Hence, statement ( 1 ) is correct. (2) ∣adj⁡(A)∣=∣A−1⋅∣A∣|\operatorname{adj}(A)|=\left|A^{-1} \cdot\right| A \mid Hence, statement (2) is not correct.
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