\( \mathrm{A}=\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & ...

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\( \mathrm{A}=\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end{array}\right] \) is a matrix satisfying the equation \( \mathrm{AA}^{\mathrm{T}}=9 \mathrm{I} \), where \( \mathrm{I} \) is \( 3 \times 3 \) matrix, then the ordered pair \( (a, b) \) is equal to
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