Matrices and Determinants

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