Wow! Crazy cryptogram!

Logic Level 2

\[ \begin{array}{ccccc} & & & & A&B\\ \times & & & & A &A \\ \hline & & B & A & A &B \end{array} \]

Solve the above cryptogram. What is the first two-digit number in the product above, \(\overline{AB}\)?

Note: A number cannot start with 0, so A and B are non-zero.

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