Let \(A = \left[ {\begin{array}{*{20}{c}} 2&b&1\\ b&{{b^2} + 1}&b\\ 1&b&2 \end{array}} \right]\) where b > 0. Then the minimum value of \(\frac{{det\left( {\rm{A}} \right)}}{{\rm{b}}}\)is:
1
\(2\sqrt 3 \)
2
\(- 2\sqrt 3\)
3
\(- \sqrt 3 \)
4
\(\sqrt 3 \)