A square matrix `[a_(ij)]` such that `a_(ij)=0` for `i ne j and a_(ij) = k` where k is a constant for i = j is called :

Options

A. diagonal matrix, but not scalar matrix
B. scalar matrix
C. unit matrix
D. None of the above

Explanation

To solve the question, we need to identify the type of square matrix defined by the conditions given:

1. **Understanding the Matrix Definition**:
The matrix \( A = [a_{ij}] \) is defined such that:
- \( a_{ij} = 0 \) for \( i \neq j \) (this means all off-diagonal elements are zero).
- \( a_{ij} = k \) for \( i = j \) (this means all diagonal elements are equal to a constant \( k \)).

2. **Forming the Matrix**:
Let's consider a 3x3 matrix as an example:
\[ A = \begin{bmatrix} k & 0 & 0 \\ 0 & k & 0 \\ 0 & 0 & k \end{bmatrix} \]
Here, all diagonal elements are \( k \) and all off-diagonal elements are 0.

3. **Identifying the Type of Matrix**:
- A matrix where all off-diagonal elements are zero and diagonal elements are equal is known as a **scalar matrix**.
- A scalar matrix is a special case of a diagonal matrix where all diagonal elements are the same.

4. **Conclusion**:
Based on the definition and the structure of the matrix, we can conclude that the matrix described in the question is a **scalar matrix**.

### Final Answer:
The square matrix \( [a_{ij}] \) described is called a **scalar matrix**.

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