Number of Possible Matrices of Order 3x3 with Entries Zero or One

To determine the number of possible matrices of order 3x3 with each entry being either zero or one, we need to consider each entry in the matrix individually. Since each entry can have two possibilities (zero or one), there are a total of 2^9 (2 raised to the power of 9) different combinations for the entries in the matrix.

Explanation:

Breaking Down the Matrix:
A 3x3 matrix consists of 9 entries, which are arranged in 3 rows and 3 columns. Let's label the entries as follows:

| a b c |
| d e f |
| g h i |

Determining the Possibilities:
Each entry in the matrix can be either zero or one. Therefore, there are two possibilities for each of the 9 entries. We can consider each entry as a binary choice, where zero represents the absence of an element and one represents the presence of an element.

Calculating the Total Number of Combinations:
Since there are 2 possibilities for each entry and a total of 9 entries, we can calculate the total number of combinations using the exponentiation rule. Thus, the number of possible matrices is 2^9.

Result:
The number of possible matrices of order 3x3 with each entry being either zero or one is 2^9, which equals 512.

Visually Appealing Summary:
- A 3x3 matrix consists of 9 entries.
- Each entry can be either zero or one.
- There are 2 possibilities for each entry.
- Using the exponentiation rule, the total number of combinations is 2^9.
- Therefore, the number of possible matrices is 512.