A random process related to a random walk on upper triangular matrices over a finite field

This article considers a random process related to a random walk on n by n upper triangular matrices over a finite field Fq where q is an odd prime. The walk starts with the identity, and at each step, i is selected at random from {2,…,n} and either row i or the negative of row i is added to row i−1. This article shows that, for a given q, it takes order n2 steps for the last column to get close to uniformly distributed over all possibilities for that column.