State with reason, whether the following are true of false. A, B and C are matrices of order `2 xx 2`.
A+B=B+A

Answer

To determine whether the statement \( A + B = B + A \) is true or false for matrices \( A \) and \( B \) of order \( 2 \times 2 \), we can follow these steps:

### Step 1: Understand Matrix Addition
Matrix addition is defined such that if you have two matrices \( A \) and \( B \) of the same order, you can add them together by adding their corresponding elements.

### Step 2: Check the Commutative Property
The commutative property states that for any two numbers (or in this case, matrices), the order in which you add them does not affect the sum. This means:
\[ A + B = B + A \]

### Step 3: Apply the Commutative Property to Matrices
For matrices \( A \) and \( B \) of order \( 2 \times 2 \), we can express them as:
\[ A = \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}, \quad B = \begin{pmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{pmatrix} \]
When we add \( A \) and \( B \):
\[ A + B = \begin{pmatrix} a_{11} + b_{11} & a_{12} + b_{12} \\ a_{21} + b_{21} & a_{22} + b_{22} \end{pmatrix} \]
Similarly, adding \( B \) and \( A \):
\[ B + A = \begin{pmatrix} b_{11} + a_{11} & b_{12} + a_{12} \\ b_{21} + a_{21} & b_{22} + a_{22} \end{pmatrix} \]
Since addition of real numbers is commutative, we have:
\[ a_{ij} + b_{ij} = b_{ij} + a_{ij} \quad \text{for all } i,j \]
Thus, it follows that:
\[ A + B = B + A \]

### Conclusion
Since we have shown that \( A + B = B + A \) holds true for any \( 2 \times 2 \) matrices \( A \) and \( B \), we conclude that the statement is **True**.