Question
Let $k$ be a positive real number and let $\mathrm{A}=\left[\begin{array}{ccc}2 k-1 & 2 \sqrt{k} & 2 \sqrt{k} \\ 2 \sqrt{k} & 1 & -2 k \\ -2 \sqrt{k} & 2 k & -1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ccc}0 & 2 k-1 & \sqrt{k} \\ 1-2 k & 0 & 2 \sqrt{k} \\ -\sqrt{k} & -2 \sqrt{k} & 0\end{array}\right]$ If det $(\operatorname{adj} A)+\operatorname{det}(\operatorname{adj} B)=10^6$, then $[\mathrm{k}]$ is equal to $[$ Note : adj $\mathrm{M}$ denotes the adjoint of a square matrix $\mathrm{M}$ and $[\mathrm{k}]$ denotes the largest integer less than or equal to $\mathrm{k}$ ].