discrete structures

Let A = [a_ij] be a matrix, where a_ij are real numbers, for 1 lessthanorequalto i lessthanorequalto n and 1 lessthanorequalto j lessthanorequalto m. We consider two different specifications of when a subset X of entries a_ij in A is considered to be independent. (a) X is independent when, for each column, there is at most one element of X in this column. (b) X is independent when, for each column, there is at most one element of X in this column, and, for each row, there is at most one element of X in this row. We want to find a maximal independent set X of entries of A (in the sense of inclusion) minimizes the sum of entries in X. To this end, we use the greedy algorithm. For which of these specifications of independence is the greedy algorithm correct for all matrices A