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$ identity 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} $