JBMO-SL 2004 C2

Given $m \times n$ table, each cell signed with "-". The following operations are

(i) to change all the signs in entire row to the opposite, i. e. every "-" to "+", and every "+" to "-";

(ii) to change all the signs in entire column to the opposite, i. e. every "-" to "+" and every "+" to " -".

(a) Prove that if $m=n=100$, using the above operations one can not obtain 2004 signs "t".

(b) If $m=1004$, find the least $n>100$ for which 2004 signs " + " can be obtained.