If \(A_k=\left[\begin{array}{cc} k-1 & k \\ k-2 & k+1 \end{array}\right] \), then what is det(A1) + det(A2) + det(A3) + ... + det(A100) equal to ?

1
100
2
1000
3
9900
4
More than one of the above
5
None of the above

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