system matrix:
I'm not sure where to start. Should I switch row 3 and row 1?
Your first objective, in row reduction, is to get a "1" in the first column, first row. Yes, you can do that by swapping the first and third rows (which is a row operation). In general, as long as the number already is "first column, first row" is not 0, you can get a "1" there by dividing the entire row by that number (here, "a") but for this problem swapping rows is simpler.