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 :

Question

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 :

$(2, 1)$