Final answer:
The sign of A + B depends on the signs of A and B, and the relationship between their magnitudes.
Step-by-step explanation:
In this question, we are asked to determine the sign of A + B. Based on the given equation A + B = B + A, we can see that addition of numbers is commutative, meaning the order of the numbers does not affect the result. Therefore, the sign of A + B will be the same as the sign of B + A, which means the sign will be the same for A and B.
Let's consider the different cases:
- If A and B are both positive numbers, then their sum A + B will also be positive.
- If A and B are both negative numbers, then their sum A + B will also be negative.
- If A is positive and B is negative, or vice versa, then their sum A + B will depend on the magnitude of the numbers. The sum will have the sign of the number with the larger magnitude.
Therefore, the sign of A + B depends on the signs of A and B, and the relationship between their magnitudes.