RU-ALLRUSSIAN 1968 Problem 12

(a) Given a $4 \times 4$ array with $+$ signs in each place except for one non-corner square on the perimeter which has a - sign. You can change all the signs in any row, column or diagonal. A diagonal can be of any length down to 1. Prove that it is not possible by repeated changes to arrive at all $+$ signs.

(b) What about an $8 \times 8$ array?