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 will analyze the properties of matrix subtraction.

### Step-by-Step Solution:

1. **Understanding Matrix Subtraction**:
- Matrix subtraction is defined as the element-wise subtraction of corresponding elements of two matrices.
- For two matrices \( A \) and \( B \) of the same order, the subtraction \( A - B \) is performed as follows:
\[ A - B = \begin{pmatrix} a_{11} - b_{11} & a_{12} - b_{12} \\ a_{21} - b_{21} & a_{22} - b_{22} \end{pmatrix} \]
- Similarly, \( B - A \) is computed as:
\[ B - A = \begin{pmatrix} b_{11} - a_{11} & b_{12} - a_{12} \\ b_{21} - a_{21} & b_{22} - a_{22} \end{pmatrix} \]

2. **Comparing \( A - B \) and \( B - A \)**:
- From the definitions above, we can see that:
\[ A - B = \begin{pmatrix} a_{11} - b_{11} & a_{12} - b_{12} \\ a_{21} - b_{21} & a_{22} - b_{22} \end{pmatrix} \]
\[ B - A = \begin{pmatrix} b_{11} - a_{11} & b_{12} - a_{12} \\ b_{21} - a_{21} & b_{22} - a_{22} \end{pmatrix} \]

3. **Analyzing the Equality**:
- For \( A - B \) to equal \( B - A \), the following must hold true for each corresponding element:
\[ a_{ij} - b_{ij} = b_{ij} - a_{ij} \quad \text{for all } i, j \]
- Rearranging gives:
\[ a_{ij} - b_{ij} + a_{ij} - b_{ij} = 0 \implies 2(a_{ij} - b_{ij}) = 0 \implies a_{ij} = b_{ij} \]
- This means that \( A \) must be equal to \( B \) for the equation \( A - B = B - A \) to hold.

4. **Conclusion**:
- Since \( A \) and \( B \) are arbitrary \( 2 \times 2 \) matrices, it is not generally true that \( A = B \). Therefore, the statement \( A - B = B - A \) is **false**.

### Final Answer:
The statement \( A - B = B - A \) is **false** because matrix subtraction is not commutative.