KöMaL 2017 K531

Let us consider a $4\times 4$ chessboard. In each step, the colour of every square in a chosen $2\times 2$ block is changed (black to white, and white to black). $a)$ By performing some of these steps, is it possible to obtain a completely black board? $b)$ Is this possible in the case of a $5\times 5$ board, provided that the corners are initially white?