Here we examine Dodgson's Method, a fraction-free methods for computing determinants. In some cases, this method fails due to division by zero. We propose a workaround for Dodgson's Method that ensures it also can be used to compute the determinant of any integer matrix.
Leggett, Deanna and Perry, John, "Fraction-Free Computation of Determinants" (2011). Mathematics Student Presentations. Paper 1.