Matrix calculation in logic algebra

Using the modulo two addition operation, the fundamental concepts of matrix calculus are defined in the logic algebra, such as linearly dependent and independent sets of rows (columns) of a matrix, matrix rank, sum and product of matrices, matrix determinant, inverse matrix. The properties of the determinants of the logic algebra are given. Using inverse matricesof the logic algebra,systems of linear equations with modulo two sums are solved. Examples are given for calculating the rank of a matrix, determinants, inverse matrices and solving systems of linear equations with modulo two sums in the logic algebra.