Maximum number of non-zero entries ,such that no two non-zero entries are on the same row or column.

Question

In an M x N matrix such that all non-zero entries are covered in "a" rows and " b" columns. Then the maximum number of non-zero entries ,such that No two non-zero entries are on the same row or column is S. Then:-

A) S <=(a+b)

B) S <=max (a,b)

C) S <= min (M-a,N-b)

D) S <= min (a,b)

I tried to solve it using some examples & was able to discard the options C & D but can't decide between options A & B. I also figured out that the required S is the Rank of the Matrix (Correct me if I'm wrong).

One of the examples I took : M=4 , N=3 , a=1 , b=3 -----> S =3

                        | 1 0 0 |
                        | 0 1 0 |
                        | 0 0 1 |
                        | 0 0 0 | 

Please, tell me how to solve it. Is there any other way crack this problem ?