Black and White points on a grid

Question

Some points on (integer, rectangular) grid in a plane are colored white, some black and some are not colored.
In each step, one vertical or horizontal line can be selected, and all colored points on that line would toggle their color.
Prove there is a finite sequence of steps after which on every vertical or horizontal line number of black and number of white points differs by 1 at most.

Answer 1

What sequence of horizontal or vertical steps would lead

B W

W W

to have the number of black and white points almost even?