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

Question

$\begin{array}{1 1} (2,-1)\\ (-2,1) \\ (2,1) \\ (-2,-1) \end{array} $