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