IIT-JEE 2010 · Paper 2, Mathematics question 30

Let $k$ be a positive real number and let $$A=\begin{bmatrix}2k-1&2\sqrt k&2\sqrt k\\2\sqrt k&1&-2k\\-2\sqrt k&2k&-1\end{bmatrix}\ \text{ and }\ B=\begin{bmatrix}0&2k-1&\sqrt k\\1-2k&0&2\sqrt k\\-\sqrt k&-2\sqrt k&0\end{bmatrix}.$$ If $\det(\operatorname{adj}A)+\det(\operatorname{adj}B)=10^6$, then $[k]$ is equal to

[Note: adj M denotes the adjoint of a square matrix M and $[k]$ denotes the largest integer less than or equal to $k$].