my %zero_columns;
  @zero_columns{ 0 .. $#{$rows[0]} } = (); # initially, all columns might have 0.

  # eliminate any columns that have non-0 in any row:
  for ( my $r = 0; $r <= $#rows && keys %zero_columns; $r++ ) {
    for my $i ( keys %zero_columns ) {
      $rows[$r][$i] == 0 or delete $zero_columns{$i};
    }
  }

  # invert the set:
  my @non_zero_columns = grep {
    ! exists $zero_columns{$_}
  } 0 .. $#{$rows[0]};