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

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