Identify scalar matrix from the following matrices.

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