Digit Multiplication Time!

Algebra Level 2

Let \(A\) be a positive single-digit number, such that:

  • \(A^2\) is single-digit number.
  • \(\overline{AA}^2\) is four-digit number.

What is \(\overline{AAA}^2\)?

Note: The leading digits for both \(A^2\) and \(\overline{AA}^2\) are nonzero.

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