Go magnet patent

A, the attraction of chessboard to chessboard is equal to the attraction of chessboard to chessboard, so A is wrong;

B, the attraction of the chessboard to the chessboard is opposite to the attraction of the chessboard, so B is wrong;

C, the chess piece is subjected to vertical downward gravity, the upward friction is static and in a state of balance, and the friction suffered by the chess piece is equal to the gravity of the chess piece, so c is wrong;

D, friction and the gravity of the chess piece are a pair of balancing forces, which are equal in size, so D is correct;

So choose D.