If A and B are square matrices of same order, then which of the following is true -

Options

A. A-B = B-A
B. A+B = B-A
C. A+B = B+A
D. None of these

Explanation

To solve the problem, we need to analyze the properties of square matrices A and B of the same order. We will evaluate the given options to determine which statement is true.

### Step-by-Step Solution:

1. **Understanding the Properties of Matrices**:
- We know that matrices can be added and multiplied, but they do not generally follow the same properties as real numbers. However, there are certain properties that hold true for matrix addition and multiplication.

2. **Evaluate Option 1: \( AB, A - B = B - A \)**:
- This option suggests that the difference of two matrices A and B is equal to the negative of the difference in reverse order.
- Let's analyze:
\[ A - B = - (B - A) \]
This is a true statement, but it does not imply that \( A - B = B - A \). Therefore, this option is **not correct**.

3. **Evaluate Option 2: \( A + B = B + A \)**:
- This option states that the sum of two matrices is commutative.
- We can prove this by taking two matrices:
Let \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \) and \( B = \begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix} \).
- Calculate \( A + B \):
\[ A + B = \begin{pmatrix} 1 + 2 & 2 + 3 \\ 3 + 4 & 4 + 5 \end{pmatrix} = \begin{pmatrix} 3 & 5 \\ 7 & 9 \end{pmatrix} \]
- Now calculate \( B + A \):
\[ B + A = \begin{pmatrix} 2 + 1 & 3 + 2 \\ 4 + 3 & 5 + 4 \end{pmatrix} = \begin{pmatrix} 3 & 5 \\ 7 & 9 \end{pmatrix} \]
- Since \( A + B = B + A \), this option is **correct**.

4. **Conclusion**:
- After evaluating both options, we conclude that the only true statement is:
\[ A + B = B + A \]