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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. Statement 1 and 2 are correct We know that if AA ^ T =1 then, A is called orthogonal matrix But, AA ^ T = A (- A )=- A ^2 [ A ^ T =- A ] Statement 3 is not correct.

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