📘 Question
The matrix
\[
A =
\begin{bmatrix}
0 & -5 & 8 \\
5 & 0 & 12 \\
-8 & -12 & 0
\end{bmatrix}
\]
is a:
(a) diagonal matrix
(b) symmetric matrix
(c) skew-symmetric matrix
(d) scalar matrix
✏️ Step-by-Step Solution
Step 1: Check definition
A matrix is skew-symmetric if:
\[
A^T = -A
\]
—
Step 2: Compare elements
- \(a_{12} = -5,\; a_{21} = 5\)
- \(a_{13} = 8,\; a_{31} = -8\)
- \(a_{23} = 12,\; a_{32} = -12\)
- Diagonal elements = 0
Step 3: Conclusion
Matrix is skew-symmetric.
—✅ Final Answer
\[
\boxed{(c)\; \text{skew-symmetric matrix}}
\]
—
💡 Key Concept
- Diagonal elements are always zero
- Opposite elements are negatives