Correcting matrix products over the ring of integers

Let A, B, and C be three n× n matrices. We investigate the problem of verifying whether AB=C over the ring of integers and finding the correct product AB. Given that C is different from AB by at most k entries, we propose an algorithm that uses O(√kn2+k2n) operations. Let α be the largest absolute value of an entry in A, B, and C. The integers involved in the computation are of O(n3α2).