In the following sum, the letters represent distinct digits from 0 to 9. Find them, giving reasons behind each step you perform.
 Further, is your solution unique? Why or why not? 

To solve the given sum, let's represent the digits with variables and apply basic addition rules to find the values of each letter. The sum is:

\[
\begin{bmatrix} A & B & C \\ + B & A & C \end{bmatrix}
\]

Where \(A\), \(B\), and \(C\) are distinct digits from 0 to 9. Let's break down the solution step by step:

1. Write the Sum:
   \[
   \begin{align*}
   &\phantom{+}\ A\ B\ C \\
   &+\ \phantom{0}\ B\ A\ C \\
   \end{align*}
   \]

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