b
$\left| {{{\rm{A}}_\lambda }} \right| = \left| {\begin{array}{*{20}{c}}
\lambda &{\lambda - 1}\\
{\lambda - 1}&\lambda
\end{array}} \right| = {\lambda ^2} - {[\lambda - 1)^2}$
$ = 2\lambda - 1$
$\therefore \left| {{{\rm{A}}_1}} \right| + \left| {{{\rm{A}}_2}} \right| + \left| {{{\rm{A}}_3}} \right| + \ldots . + \left| {{{\rm{A}}_{300}}} \right|$
$=1+3^{2}+5+\ldots . .+599 $
$= \frac{300}{2}(1+599)=(300)^{2} $