The function
Part can be useful, because it allows access to the rows and columns of a matrix. For example, mat[[1]] returns the first row, and mat[[All, 1]] is the first column. Assignments are also possible, e.g. mat[[1]] = mat[[1]] - 2 mat[[2]] will modify the matrix in place by subtracting twice the second row from the first one.
This
tutorial from the documentation may be of interest, as well as this related
discussion on the Mathematica StackExchange site.