The matrix \(A=\begin{bmatrix} 0 & -5 & 8\\ 5 & 0 & 12\\ -8 & -12 & 0\end{bmatrix}\) is a
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → skew symmetric matrix
A matrix is skew symmetric when \(A^T = -A\), that is \(a_{ji} = -a_{ij}\) for all i, j; then every diagonal entry is 0.
Here the diagonal entries are all 0, and
\(a_{12} = -5,\quad a_{21} = 5\)
\(a_{13} = 8,\quad a_{31} = -8\)
\(a_{23} = 12,\quad a_{32} = -12\)
So \(A^T = -A\) and A is skew symmetric. It is not symmetric (\(a_{12} \ne a_{21}\)), and it is neither diagonal nor scalar, because its off-diagonal entries are not zero.