x11 + x12 + x13
    = (x + y) + (x - z) + (x - y + z)
    = 3x

  x21 + x22 + x23
    = (x - 2y + z) + (x) + (x + 2y - z)
    = 3x

  x31 + x32 + x33
    = (x + y - z) + (x + z) + (x - y)
    = 3x

  x11 + x21 + x31
    = (x + y) + (x - 2y + z) + (x + y - z)
    = 3x

  x12 + x22 + x32
    = (x - z) + (x) + (x - z)
    = 3x

  x13 + x23 + x33
   = (x - y + z) + (x + 2y - z) + (x - y)
   = 3x

  x11 + x22 + x33
   = (x + y) + (x) + (x - y)
   = 3x

  x13 + x22 + x31
   = (x - y + z) + (x) + (x + y - z)
   = 3x