Chess and Tetraminoes

Tetraminoes are these useful tiles you use in tetris. This is how they somewhat look like (forgive me for the crappy graphic):

Given that you have infinite tetraminoes, and tiles cannot overlap;

(a)Can you cover a chessboard (8x8) with tetraminoes?
(b)We take the chessboard, and remove the top-left square and the one to its right (A8, B8); along with the bottom-right square and the one to its left (G1, H1) and by that create a crippled chessboard. Can you cover the crippled chessboard with tetraminoes? Following is a sketch of a crippled board.

PS: It helps to solve the one with the Dominoes first