📘 Question
The matrix
\[
A =
\begin{bmatrix}
1 & 0 & 0 \\
0 & 2 & 0 \\
0 & 0 & 4
\end{bmatrix}
\]
is a:
(a) identity matrix
(b) symmetric matrix
(c) skew-symmetric matrix
(d) diagonal matrix
✏️ Step-by-Step Solution
Step 1: Observe matrix
All non-diagonal elements are zero.
—Step 2: Check definitions
- Identity matrix: diagonal elements must be 1 → ❌ (here 2, 4)
- Symmetric matrix: \(A^T = A\) → ✔ but not most specific
- Skew-symmetric: diagonal must be zero → ❌
- Diagonal matrix: only diagonal elements non-zero → ✔
Step 3: Conclusion
Matrix is a diagonal matrix.
—✅ Final Answer
\[
\boxed{(d)\; \text{diagonal matrix}}
\]
—
💡 Key Concept
- Diagonal matrix → non-diagonal elements = 0
- Identity matrix → diagonal elements = 1