Discussion
The matrix \(\begin{bmatrix} 0 & 2 & -3 \\ -2 & 0 & 4 \\ 3 & -4 & 0 \end{bmatrix}\) is
Answer: C
The matrix is skew symmetric.
A matrix is skew symmetric when \(A^{T} = -A\), that is \(a_{ji} = -a_{ij}\) for every pair, which forces every diagonal entry to be zero. Here the diagonal is 0, 0, 0 and each mirrored pair has opposite signs: \(a_{12} = 2\) and \(a_{21} = -2\); \(a_{13} = -3\) and \(a_{31} = 3\); \(a_{23} = 4\) and \(a_{32} = -4\).
It is not symmetric, because that needs \(a_{ji} = a_{ij}\). It is not diagonal, since its off-diagonal entries are non-zero, and it is not triangular, because it has non-zero entries both above and below the diagonal.
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