From the formula for the determinant, we see that every non diagonal element of the matrix 1 + t A will be multiplied by other non diagonal elements and thus will be of order at least t 2. And for the term with only diagonal elements, we have: i(1 + t Aii) = 1 + ttraceA + O(t 2), where the second term corresponds to choosing one Aii in the product and 1 for all the other factors. Choosing two or more Aiis gives a term O(t 2).