VTRMC 2010 Problem 1

Let $d$ be a positive integer and let $A$ be a $d\times d$ matrix with integer entries. Suppose $I+A+A_2+\ldots+A_{100}=0$ (where $I$ denotes the identity $d\times d$ matrix, and $0$ denotes the zero matrix, which has all entries $0$ ). Determine the positive integers $n\le100$ for which $A_n+A_{n+1}+\ldots+A_{100}$ has determinant $\pm1$ .