📘 Question
The matrix
\[
A =
\begin{bmatrix}
0 & 0 & 4 \\
0 & 4 & 0 \\
4 & 0 & 0
\end{bmatrix}
\]
is a:
(a) square matrix
(b) diagonal matrix
(c) unit matrix
(d) none of these
✏️ Step-by-Step Solution
Step 1: Check order
Matrix has 3 rows and 3 columns:
\[
3 \times 3
\]
✔ So it is a square matrix.
—
Step 2: Check diagonal matrix
Diagonal matrix must have all non-diagonal elements = 0. Here non-diagonal elements like 4 exist ❌
—Step 3: Check unit matrix
Unit matrix must have 1’s on diagonal only ❌
—Step 4: Conclusion
Only condition satisfied is square matrix.
✅ Final Answer
\[
\boxed{(a)\; \text{square matrix}}
\]
💡 Key Concept
- Square matrix: rows = columns
- Diagonal matrix: non-diagonal elements = 0
- Unit matrix: diagonal elements = 1