`{:(" 1 2 A"),("+6 A B"),(---),(" A 0 9"),(---):}`

Answer

To solve the problem where we need to find the values of \( a \) and \( b \) in the addition problem:

```
1 2 A
+ 6 A B
-------
A 0 9
```

we can follow these steps:

### Step 1: Analyze the addition
From the addition, we can see that the last digit of the result is 9. This means that the sum of \( A \) and \( B \) must equal 9, or it could be 19 if there is a carry from the previous column. We can write this as:
\[ A + B = 9 \quad \text{(Equation 1)} \]

### Step 2: Analyze the second column
Next, we look at the second column from the right, where we have \( 2 + A \). The result in this column is 0, which means:
\[ 2 + A = 0 \quad \text{or} \quad 2 + A = 10 \]
Since \( A \) is a digit (0-9), \( 2 + A = 0 \) is not possible. Therefore, we have:
\[ 2 + A = 10 \quad \text{(Equation 2)} \]

### Step 3: Solve Equation 2
From Equation 2, we can solve for \( A \):
\[ A = 10 - 2 \]
\[ A = 8 \]

### Step 4: Substitute \( A \) into Equation 1
Now that we have \( A \), we can substitute it into Equation 1 to find \( B \):
\[ 8 + B = 9 \]
\[ B = 9 - 8 \]
\[ B = 1 \]

### Final Answer
Thus, the values of \( A \) and \( B \) are:
\[ A = 8 \]
\[ B = 1 \]

### Summary
The final answer is:
- \( A = 8 \)
- \( B = 1 \)

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