If A and B are square martrices of equal degree, then which one
is correct among the following?

Options

A. A+B=B+A
B. A+B=A-B
C. A-B=B-A
D. AB=BA

Answer

To solve the question, we need to analyze the properties of square matrices and determine which of the given options is correct.

### Step-by-step Solution:

1. **Understanding the Properties of Matrix Addition:**
- Matrix addition is commutative. This means that for any two square matrices \( A \) and \( B \) of the same size, the following holds:
\[ A + B = B + A \]

2. **Analyzing Option 1:**
- The first option states:
\[ A + B = B + A \]
- Since we established that matrix addition is commutative, this option is correct.

3. **Analyzing Option 2:**
- The second option states:
\[ A + B = A - B \]
- This is generally not true. The left side represents the sum of matrices, while the right side involves subtraction. Therefore, this option is incorrect.

4. **Analyzing Option 3:**
- The third option states:
\[ A - B = B - A \]
- This is also not true as subtraction of matrices is not commutative. Therefore, this option is incorrect.

5. **Analyzing Option 4:**
- The fourth option states:
\[ AB = BA \]
- This is not generally true for matrix multiplication. Matrix multiplication is not commutative in general. Therefore, this option is incorrect.

### Conclusion:
After analyzing all the options, we conclude that the only correct statement is from Option 1:
\[ A + B = B + A \]

### Final Answer:
The correct option is **Option 1**.

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