1. The problem is to identify the property used in the equation $A + (-A) = 0$. 2. This equation shows that when you add a number and its additive inverse (the negative of the number), the result is zero. 3. The property used here is called the **Additive Inverse Property**. 4. The Additive Inverse Property states that for every number $A$, there exists a number $-A$ such that: $$A + (-A) = 0$$ 5. This property is fundamental in algebra and helps in solving equations by canceling terms. 6. Therefore, the equation $A + (-A) = 0$ demonstrates the Additive Inverse Property.