Chapter 15: Binary Matrices

An m × n matrix A is a binary matrix if a_jk ∈ {0, 1} for j = 1, … ,m and k = 1, … , n. A binary matrix is a matrix over the two-element field GF(2) = {0, 1}. In GF(2) = {0, 1} we have that −1 = 1, i.e. 1 + 1 = 0. Thus A + A = 0 for all binary matrices A, where 0 is the zero matrix. The special linear group and general linear group coincide over GF(2), GL_n(GF(2)) = SL_n(GF(2)). The set of invertible 2 × 2 binary matrices SL₂(GF(2)) is