How to do matrix conversions by row and columns toggles?

Question

I have got a square matrix consisting of elements either 1 or 0. An ith row toggle toggles all the ith row elements (1 becomes 0 and vice versa) and jth column toggle toggle

Answer 1

If you can only toggle the rows, and not the columns, then there will only be a subset of matrices that you can convert into the final result. If this is the case, then it would be very simple:

for every row, i:
  if matrix1[i] == matrix2[i]
    continue;
  else
    toggle matrix1[i];
    if matrix1[i] == matrix2[i]
      continue
    else
      die("cannot make similar");