Let $n \geq 2$ be an integer. Consider an $n\times n$ chessboard with the usual chessboard colouring. A move consists of choosing a $1\times 1$ square and switching the colour of all squares in its row and column (including the chosen square itself). For which $n$ is it possible to get a monochrome chessboard after a finite sequence of moves?
Now For n=2x just select a random Color and do the procces On all of the Squares of that Color.
Notice that the difference between black and white squares stays constant mod 2, hence all n with are odd don’t work.