NDA 2024 Mathematics question

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

(A)1 and 2 onlyCorrect
(B)2 and 3 only
(C)1 and 3 only
(D)1, 2 and 3

Answer: (A)

Solution

For a skew-symmetric matrix ; putting gives , so every diagonal element is zero (statement 1) and hence their sum is zero (statement 2). A

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Question ID VK-029787