If A = `(a_(ij))_(2xx2)` where `a_(ij) = i+j` then A is equal to

Options

A. `[(1,1),(2,2)]`
B. `[(1,2),(1,2)]`
C. `[(1,4),(3,3)]`
D. `[(2,3),(3,4)]`

Answer

To find the matrix \( A \) defined by \( a_{ij} = i + j \) for a \( 2 \times 2 \) matrix, we will calculate each element of the matrix step by step.

### Step-by-Step Solution:

1. **Define the Matrix Order**:
The matrix \( A \) is of order \( 2 \times 2 \). This means it has 2 rows and 2 columns.

2. **Identify the Elements**:
The elements of the matrix \( A \) are defined as \( a_{ij} = i + j \), where \( i \) is the row index and \( j \) is the column index.

3. **Calculate Each Element**:
- For \( a_{11} \) (1st row, 1st column):
\[ a_{11} = 1 + 1 = 2 \]
- For \( a_{12} \) (1st row, 2nd column):
\[ a_{12} = 1 + 2 = 3 \]
- For \( a_{21} \) (2nd row, 1st column):
\[ a_{21} = 2 + 1 = 3 \]
- For \( a_{22} \) (2nd row, 2nd column):
\[ a_{22} = 2 + 2 = 4 \]

4. **Construct the Matrix**:
Now we can construct the matrix \( A \) using the calculated elements:
\[ A = \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix} = \begin{pmatrix} 2 & 3 \\ 3 & 4 \end{pmatrix} \]

### Final Result:
Thus, the matrix \( A \) is:
\[ A = \begin{pmatrix} 2 & 3 \\ 3 & 4 \end{pmatrix} \]