If A_k=\left[\begin{array}{cc}k-1 & k \ k-2 & k+1]\end{array}, then what is {\det} (\bo {A}_1) +{\det} (\bo {A}_2) +{\det} (\bo {A}_3) +. . .+{\det} (\bo {A}_{100}) equal to? [NDA II 2023]