How many matrices of order 2 x 2 are possible with entry 2 × 2.

Answer

To find out how many matrices of order 2 x 2 can be formed with entries 1 and 2, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Order of the Matrix**:
- The order of the matrix is given as 2 x 2.
- This means the matrix will have 2 rows and 2 columns.

2. **Calculate the Total Number of Elements**:
- The total number of elements in a 2 x 2 matrix is calculated as:
\[ 2 \times 2 = 4 \]
- So, there are 4 positions in the matrix that need to be filled.

3. **Identify the Possible Entries**:
- The entries that can be used in the matrix are given as 1 and 2.
- Therefore, we have 2 possible entries.

4. **Determine the Number of Ways to Fill the Matrix**:
- Since each of the 4 positions in the matrix can be filled with either 1 or 2, and since we can repeat the entries, we can use the formula for combinations with repetition.
- The total number of ways to fill the matrix is given by:
\[ \text{Number of entries}^{\text{Number of elements}} = 2^4 \]

5. **Calculate the Total Number of Matrices**:
- Now, we calculate \(2^4\):
\[ 2^4 = 16 \]
- Therefore, the total number of matrices of order 2 x 2 that can be formed with entries 1 and 2 is 16.

### Final Answer:
The total number of matrices of order 2 x 2 possible with entries 1 and 2 is **16**.