A square matrix A has 9 elements. What is the possible order of A?

Options

A. `1xx9`
B. `9xx9`
C. `3xx3`
D. `2xx7`

Answer

To determine the possible order of a square matrix \( A \) that has 9 elements, we need to understand the relationship between the number of elements in a square matrix and its order.

### Step-by-Step Solution:

1. **Understanding Square Matrices**:
A square matrix is defined as a matrix with the same number of rows and columns. If a square matrix has an order of \( n \times n \), it will have \( n^2 \) elements.

2. **Setting Up the Equation**:
Given that the matrix has 9 elements, we can set up the equation:
\[ n^2 = 9 \]

3. **Solving for \( n \)**:
To find \( n \), we take the square root of both sides:
\[ n = \sqrt{9} \]
\[ n = 3 \]

4. **Conclusion**:
Therefore, the possible order of the square matrix \( A \) is \( 3 \times 3 \).

### Final Answer:
The possible order of matrix \( A \) is \( 3 \times 3 \).

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