`A=[a_(ij)]_(mxxn)` is a square matrix, if

Options

A. `mltn`
B. `mgtn`
C. `m=n`
D. None of these

Answer

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 a matrix in which 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 Given Matrix**:
In our case, we have a matrix \( A \) of order \( m \times n \). For \( A \) to be a square matrix, we need to check the relationship between \( m \) and \( n \).

4. **Setting Up the Condition**:
Since a square matrix requires that the number of rows (m) equals the number of columns (n), we can express this condition mathematically as:
\[ m = n \]

5. **Conclusion**:
Therefore, the matrix \( A \) is a square matrix if and only if \( m \) is equal to \( n \).

### Final Answer:
The condition for the matrix \( A \) to be a square matrix is:
\[ \text{m is equal to n} \]