Donald Knuth extended Baxter permutations to Baxter matrices, and asked whether there exist operations for Baxter matrices that preserve Baxterhood. In this paper, we first show that each Baxter matrix contains a row or a column with a single 1. Then we construct an operation ϕ based on the deletion of a row or a column with a single 1, and show that ϕ preserves Baxterhood. As a corollary, we obtain a new proof of a conjecture of Knuth about the maximum number of 1s in Baxter matrices.