Suppose two opposite corner squares are removed from an 8 × 8 chessboard — as in part (a)...

Suppose two opposite corner squares are removed from an 8 × 8 chessboard — as in part (a) of Fig. 2.4. Can the remaining 62 squares be covered by 31 dominos (rectangles consisting of two adjacent squares — one white and the other blue, as shown in the figure)? (When a domino is placed on the chessboard, a square of a given color need not be placed on a square of the same color.)

Figure 2.4