Toggling Colors on a Grid: Evenness Condition for Solution

On an infinite grid of squares, 100 cells are coloured black while all other cells are coloured white. In a single move, you may toggle the colour of any four cells that form a $2 \times 2$ square. Prove that it is possible to turn all cells white after a finite number of moves if and only if every row and every column contains an even number of black cells.