Matrices And Determinants

For \(i=1,2,3\) and \(j=1,23\)
If \(a_i^2+b_i^2+c_i^2=1, a_i a_j+b_i b_j+c_i c_j=0, \forall i \neq j\)
and $$A=\left[\begin{array}{lll}a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3\end{array}\right]$$, then \(\operatorname{det}\left(A A^T\right)=\)