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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Matrices

NDA 2022 · Mathematics · Matrices

Let A be a non-singular matrix and B=adj A . Which of the following...

Let AA be a non-singular matrix and B=adj⁡AB=\operatorname{adj} A. Which of the following statements is/are correct? 1. AB=BA2.A B=B A 2.A Bisascalarmatrix3.is a scalar matrix 3.A BcanbeanullmatrixSelectthecorrectanswerusingthecodegivenbelow:can be a null matrix Select the correct answer using the code given below :

Options

  1. A1 only
  2. B1 and 2 only
  3. C2 only
  4. D1, 2 and 3

Correct answer

B. 1 and 2 only

Step-by-step solution

Given that ∣A∣≠0|A| \neq 0 and B=adj⁡AAB=A(adj⁡A)=∣A∣IB=\operatorname{adj} AA B=A(\operatorname{adj} A)=|A| IBA=[adj⁡(A)]A=∣A∣I∴AB=BA\begin{aligned} & B A=[\operatorname{adj}(A)] A=|A| I \\ \therefore \quad & A B=B A\end{aligned}$So,statement1iscorrectItisclearfrom(i)So, statement 1 is correct It is clear from (i)A B$ is a scalar matrix not null matrix So statement 2 is correct and 3 is not correct.
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