If \( A=\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end...

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