Minimum Flips for Symmetric Grid

Question

Cells come in two colors, "B" for black and "W" for white, and they fill a grid of N rows with M cells each. We call a row or a column symmetric when it looks identical whether you read it forwards or backwards. A flip turns one cell to the opposite color, "B" into "W" or "W" into "B". Flip cells until every row and every column is symmetric. ...