The number of all possible matrices of order ` 3xx 3 ` with each entry 0 or 1 is

Options

A. 27
B. 18
C. 81
D. 512

Answer

To find the number of all possible matrices of order \(3 \times 3\) with each entry being either \(0\) or \(1\), we can follow these steps:

### Step-by-step Solution:

1. **Determine the size of the matrix**:
A \(3 \times 3\) matrix has \(3\) rows and \(3\) columns. Therefore, the total number of entries in the matrix is:
\[ 3 \times 3 = 9 \]

2. **Identify the choices for each entry**:
Each entry in the matrix can be either \(0\) or \(1\). This gives us \(2\) options for each entry.

3. **Calculate the total combinations**:
Since there are \(9\) entries in the matrix and each entry has \(2\) choices, the total number of possible matrices can be calculated using the formula for combinations:
\[ \text{Total matrices} = 2^{\text{number of entries}} = 2^9 \]

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

5. **Conclusion**:
Therefore, the total number of all possible \(3 \times 3\) matrices with each entry being \(0\) or \(1\) is:
\[ \boxed{512} \]