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?

For a skew-symmetric matrix, A^T = −A. The diagonal elements satisfy aᵢᵢ = −aᵢᵢ, hence aᵢᵢ = 0. Statement 1 is TRUE. Statement 2 follows directly from 1, also TRUE. Statement 3: A skew-symmetric matrix is generally NOT orthogonal (would require A^T·A = I, but A^T·A = −A·A = −A² which is not generally I). FALSE. So 1 and 2 only.