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

Explanation

In a skew-symmetric matrix, A^T = -A, which implies a_{ij} = -a_{ji}. For diagonal elements, a_{ii} = -a_{ii}, so 2a_{ii} = 0 \Rightarrow a_{ii} = 0. Statement 1 is true. Since all diagonal elements are zero, their sum is clearly zero. Statement 2 is true. A skew-symmetric matrix is not necessarily orthogonal (e.g., a zero matrix is skew-symmetric but not orthogonal). Statement 3 is false.

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