1. **State the problem:** Given the equation $a^2 - ab$, multiply both sides by $a$ and follow the steps to simplify and solve for $a$. 2. **Step-by-step solution:** - Start with the equation: $a^2 - ab$ - Multiply both sides by $a$: $a^2 - b^2 = ab - b^2$ - Subtract $b^2$ from both sides: $(a + b)(a - b) = b(a - b)$ - Factor both sides: $(a + b)(a - b) = b(a - b)$ - Divide both sides by $(a - b)$: $a + b = b$ - Subtract $b$ from both sides: $a + b - b = b - b$ - Simplify: $a = 0$ 3. **Important note:** Dividing by $(a - b)$ assumes $(a - b) \neq 0$. If $a = b$, division by zero occurs, which is undefined. Therefore, the step dividing by $(a - b)$ is invalid if $a = b$. 4. **Conclusion:** The final result $a = 0$ is only valid if $a \neq b$. Otherwise, the division step is not allowed, and the original equation must be reconsidered. **Final answer:** $a = 0$ (with the condition $a \neq b$).