Dominoes Covering

Let us colour the 2 * 1 dominoes into a black and a white pair each.Now we are cutting two diagonally opposite squares. let these two be both black (note that both has to be of same colour.).so now we have 32 white and 30 black squares on the chess board. Obviously its impossible to fill the mutilated chess board,as on placing dominoes,number of black and white squares must be equal.

Since dominoes cannot be placed diagonally, they will always cover two squares when placed; two adjacent squares (and by this I mean edges touching, not corners). Given any two adjacent squares, one is black and the other is white, so basically, a given domino will cover 1 black square and 1 white square no matter where it is placed.

Since the chess board is 8x8, we know that opposite corners will be of the same colour (imagine a 2x2 board). Thus, either two white squares are removed or two black squares are removed. Now the number of black and white tiles are not equal (ex. 30 black 32 white). Since a domino must cover a white tile and a black tile whenever it's placed, when the 30 black tiles are accounted for, so will 30 white tiles. This leaves 2 white tiles to be covered, and as stated above, this is impossible to do with a 2x1 domino.