L-tromino tiling of a chessboard

(a) A $16\times 16$ chessboard is divided into unit squares and one corner unit square is removed. Prove that the remaining board can be tiled by L-trominoes (each tromino consists of $3$ unit squares forming an L-shape).

(b) State and prove a generalisation: for every integer $n\ge 1$, a square of side $2^n$ with one corner cell removed can be tiled by L-trominoes.