Let A be the set of all `3xx3` matrices of whose entries are either 0 or 1. The number of elements is set A, is

Options

A. `2^3`
B. `2^6`
C. 18
D. `2^9`

Explanation

To find the number of elements in the set A, which consists of all \(3 \times 3\) matrices with entries that can either be 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 a total of \(3 \times 3 = 9\) positions (or entries).

2. **Identify Possible Values for Each Entry**:
Each entry in the matrix can take on one of two values: either 0 or 1.

3. **Calculate the Total Combinations**:
Since each of the 9 entries can independently be either 0 or 1, the total number of different matrices can be calculated as:
\[ \text{Total Matrices} = 2^{\text{number of entries}} = 2^9 \]

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

5. **Conclusion**:
Therefore, the number of elements in the set A is \(512\).

### Final Answer:
The number of elements in the set A is \(512\).

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