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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Matrices

NDA 2024 · Mathematics · Matrices

Consider the following statements in respect of a skew-symmetric...

Consider the following statements in respect of a skew-symmetric matrix A of order 3: 1. All diagonal elements are zero. 2. The sum of all the diagonal elements of the matrix is zero. 3. A is orthogonal matrix. Which of the statements given above are correct?

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

We have, all diagonal elements of skew symmetric matrix is zero then their sum is also zero. ∴\therefore Statement 1 and 2 are correct We know that if AAT=1\mathrm{AA}^{\mathrm{T}}=1 then, A is called orthogonal matrix But, \mathrm{AA}^{\mathrm{T}}=\mathrm{A}(-\mathrm{A})=-\mathrm{A}^2\left[\because \mathrm{A}^{\mathrm{T}}=-\mathrm{A}\right]\therefore Statement 3 is not correct.
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