Me out with will mark the first one as the brainiest answer.

You cannot add row 2 to column 3 because they have different dimensions. You can do any of the other operations, but the only one that makes any sort of sense is ...
  Multiply row 2 by -1 and add it to row 3


It makes no sense to multiply a row by zero. That makes the entire row zero and makes the matrix useless for finding any sort of solution.

You can switch columns, but that doesn't get you any closer to a solution here.

If I were trying to find a solution, I might
  switch rows 1 and 2
  multiply the new row 1 by -3 and add it to the new row 2
  multiply the new row 1 by 2 and add it to row 3
This sequence of operations will make the first column [1 0 0], reducing the problem to 2×2 from 3×3.