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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Matrices

NDA 2018 · Mathematics · Matrices

For a square matrix A , which of the following properties hold? 1....

For a square matrix A , which of the following properties hold? 1. (A−1)−1=A\left(\mathrm{A}^{-1}\right)^{-1}=\mathrm{A} 2. det⁡(A−1)=1det⁡ A\operatorname{det}\left(\mathrm{A}^{-1}\right)=\frac{1}{\operatorname{det} \mathrm{~A}} 3. (λA)−1λ A−1(\lambda \mathrm{A})^{-1} \lambda \mathrm{~A}^{-1} where λ\lambda is a scalar Select the correct answer using the code given below:

Options

  1. A1 and 2 only
  2. B2 and 3 only
  3. C1 and 3 only
  4. D1,2 and 3

Correct answer

A. 1 and 2 only

Step-by-step solution

Statement 1 and 2 are correct. Statement 3 is incorrect because (λA)−1=1λA−1,λ≠0(\lambda \mathrm{A})^{-1}=\frac{1}{\lambda} \mathrm{ A}^{-1}, \lambda \neq 0
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