At the begining there are 32 black pieces. We will prove that the number of black pieces left on the board is always even.

In the single move, we change a row or column, assume that row or column has k black pieces and 8 - k while pieces, after change all black to white and while to black, that row or column will has 8-k black and k white. The difference between black pieces after a single move is (8 - k) - k = 8 - 2k. The difference is a even (8 - 2k). Therefore, after every move, the black pieces left is alaways even and cannot be one black piece at any time.

At the begining there are 32 black pieces. We will prove that the number of black pieces left on the board is always even.

In the single move, we change a row or column, assume that row or column has k black pieces and 8 - k while pieces, after change all black to white and while to black, that row or column will has 8-k black and k white. The difference between black pieces after a single move is (8 - k) - k = 8 - 2k. The difference is a even (8 - 2k). Therefore, after every move, the black pieces left is alaways even and cannot be one black piece at any time.

At the begining there are 32 black pieces. We will prove that the number of black pieces left on the board is always even.

In the single move, we change a row or column, assume that row or column has k black pieces and 8 - k while pieces, after change all black to white and while to black, that row or column will has 8-k black and k white. The difference between black pieces after a single move is (8 - k) - k = 8 - 2k. The difference is a even (8 - 2k). Therefore, after every move, the black pieces left is alaways even and cannot be one black piece at any time.