📘 Question
Out of the following matrices, choose the matrix which is a scalar matrix:
(a) \(\begin{bmatrix}0 & 0 \\ 0 & 0\end{bmatrix}\)
(b) \(\begin{bmatrix}0 & 0 & 0 \\ 0 & 0 & 0\end{bmatrix}\)
(c) \(\begin{bmatrix}0 & 0 \\ 0 & 0 \\ 0 & 0\end{bmatrix}\)
(d) \(\begin{bmatrix}0 \\ 0 \\ 0\end{bmatrix}\)
✏️ Step-by-Step Solution
Step 1: Definition
A scalar matrix is:
- A square matrix
- Diagonal elements are equal
- All non-diagonal elements are zero
Step 2: Check options
- (a) is \(2 \times 2\), all diagonal elements equal (0) ✔
- (b) is \(2 \times 3\) → not square ❌
- (c) is \(3 \times 2\) → not square ❌
- (d) is \(3 \times 1\) → not square ❌
Step 3: Conclusion
Only option (a) satisfies scalar matrix conditions.
✅ Final Answer
\[
\boxed{(a)}
\]
💡 Key Concept
Zero matrix can also be a scalar matrix if it is square and all diagonal elements are equal.