A simple division−free algorithm for computing determinants
Richard S. Bird
We present an extremely simple method for computing determinants, one that uses no division operations, exact or otherwise. The method amounts to no more than iterating a certain matrix multiplication and requires O(nM(n)) additions and multiplications for an n×n matrix, where M(n) is the number of such operations needed for matrix multiplication. A direct combinatorial proof of correctness is given.
Information Processing Letters