`A =([a_(i j)])_(mxxn)`is a square matrix, if (a) `m < n` (b) `m > n` (c) `m =n` (d) None of these

Options

A. `m < n`
B. `m > n`
C. `m =n`
D. None of these

Explanation

To determine when a matrix \( A = [a_{ij}]_{m \times n} \) is a square matrix, we need to analyze the definitions and properties of matrices.

### Step-by-step Solution:

1. **Understanding Matrix Dimensions**:
- A matrix is defined by its dimensions, which are given in the form \( m \times n \), where \( m \) is the number of rows and \( n \) is the number of columns.

2. **Definition of a Square Matrix**:
- A square matrix is one where the number of rows is equal to the number of columns. This means that for a matrix to be square, the condition \( m = n \) must hold true.

3. **Analyzing the Options**:
- (a) \( m < n \): This indicates that there are fewer rows than columns, which cannot form a square matrix.
- (b) \( m > n \): This indicates that there are more rows than columns, which also cannot form a square matrix.
- (c) \( m = n \): This indicates that the number of rows is equal to the number of columns, which satisfies the condition for a square matrix.
- (d) None of these: This option is not applicable since we have already identified a valid condition.

4. **Conclusion**:
- The only condition under which the matrix \( A \) is a square matrix is when \( m = n \). Therefore, the correct answer is option (c).

### Final Answer:
(c) \( m = n \)