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Let \( k \) be a positive real number and let
P
\[
\begin{aligned}
\mathrm{A} & =\left[\begin{array}{ccc}
2 k-1 & 2 \sqrt{k} & 2 \sqrt{k} \\
2 \sqrt{k} & 1 & -2 k \\
-2 \sqrt{k} & 2 k & -1
\end{array}\right] \text { and } \\
\mathrm{B} & =\left[\begin{array}{ccc}
0 & 2 k-1 & \sqrt{k} \\
1-2 k & 0 & 2 \sqrt{k} \\
-\sqrt{k} & -2 \sqrt{k} & 0
\end{array}\right] .
\end{aligned}
\]
W
If \( \operatorname{det}(\operatorname{adj} \mathrm{A})+\operatorname{det}(\operatorname{adj} B)=10^{6} \), then \( [k] \) is equal to (where [.] GIF)
[IIT-JEE 2010]
(A) 3
(B) 4
(C) 5
(D) 6
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