If `a^(2)-ab=0`, which of the following is the correct conclusion?

Options

A. a=0
B. a=b
C. `a^(2)=b`
D. either a=0 or a=b

Answer

To solve the equation \( a^2 - ab = 0 \), we can follow these steps:

### Step 1: Factor the equation
We start with the equation:
\[ a^2 - ab = 0 \]
We can factor out \( a \) from the left side:
\[ a(a - b) = 0 \]

### Step 2: Set each factor to zero
According to the zero product property, if the product of two factors is zero, at least one of the factors must be zero. Therefore, we set each factor to zero:
1. \( a = 0 \)
2. \( a - b = 0 \)

### Step 3: Solve for \( b \)
From the second equation \( a - b = 0 \), we can rearrange it to find:
\[ a = b \]

### Conclusion
From the two equations we derived, we have:
1. \( a = 0 \)
2. \( a = b \)

Thus, the correct conclusion is that either \( a = 0 \) or \( a = b \).

### Final Answer
The correct conclusion is: **Either \( a = 0 \) or \( a = b \)**.

---