The total number of possible matrices of order `3xx3` with each 3 or 7 is :

Options

A. 21
B. 10
C. 512
D. 343

Answer

To determine the total number of possible matrices of order \(3 \times 3\) where each entry can either be \(3\) or \(7\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Size of the Matrix**:
The matrix is of order \(3 \times 3\), which means it has \(3\) rows and \(3\) columns.

2. **Count the Total Elements**:
The total number of elements in a \(3 \times 3\) matrix is:
\[ 3 \times 3 = 9 \]
So, there are \(9\) positions to fill in the matrix.

3. **Determine the Choices for Each Element**:
Each element of the matrix can be either \(3\) or \(7\). This gives us \(2\) choices for each of the \(9\) positions.

4. **Calculate the Total Number of Matrices**:
Since each of the \(9\) positions can independently be filled with either \(3\) or \(7\), the total number of possible matrices can be calculated using the formula:
\[ \text{Total Matrices} = 2^{\text{Number of Elements}} = 2^9 \]

5. **Compute \(2^9\)**:
Now, we calculate \(2^9\):
\[ 2^9 = 512 \]

6. **Conclusion**:
Therefore, the total number of possible matrices of order \(3 \times 3\) where each entry is either \(3\) or \(7\) is:
\[ \boxed{512} \]