Is there any basis for ‪Transversal‬ matrix space?

Question

Given That An N-By-N Matrix A, Is A Set Of Numbers With One From Each Row And Each Column Is Called A Transversal Matrix

1. Given that an n-by-n matrix A, is a set of numbers with one from each row and each column is called a transversal matrix. We say that A is a constant transversal matrix if all transversals have the same sum. If matrices A and B have the constant transversal property, then so do A+B and cA, for any constant c. Therefore it follows that the set of constant transversal matrices forms a vector space Vn. Also, the set Bn = {R_2, R_3,...R_n, C_1, C_2,..., Cn} spans Vn.

a) Show that if a row is constant of a transversal matrix then all the matrix rows are constant.

b) Let R_k be a n x n matrix in which each entry of the kth row is 1 and all other entries are 0. Show that this is a basis for the vector space Vn.