A square matrix `A=[a_(ij)]` in which `a_(ij)=0` for ` i!=j` and `[a]_(ij)=k` (constant) for `i=j` is called a

Options

A. unit matrix
B. scalar matrix
C. null matrix
D. diagonal matrix

Explanation

To solve the problem, we need to identify the type of square matrix described in the question. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Matrix Definition**:
- We are given a square matrix \( A = [a_{ij}] \).
- The matrix is defined such that \( a_{ij} = 0 \) for \( i \neq j \) (off-diagonal elements are zero).
- For the diagonal elements (where \( i = j \)), \( a_{ij} = k \), where \( k \) is a constant.

2. **Forming the Matrix**:
- Based on the definitions, the matrix \( A \) can be represented as:
\[ A = \begin{bmatrix} k & 0 & 0 & \ldots & 0 \\ 0 & k & 0 & \ldots & 0 \\ 0 & 0 & k & \ldots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \ldots & k \end{bmatrix} \]
- This matrix has \( k \) on the diagonal and zeros elsewhere.

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

4. **Conclusion**:
- Therefore, the matrix \( A \) described in the question is a **scalar matrix**.

### Final Answer:
The answer is **Option B: Scalar Matrix**.