Graph thoery ( Perfect Matchings)

Hi , I having a little problem on understanding some example that was written in my text book , so I have uploaded the page below (and written in red on it). Its todo with Applications of Matchings (Graph theory) , I understand how the graph is formed from the matrix (Matrix A that is), its just the final few lines , I am quite unsure about...... and how they quickly get A' (Matrix). If someone could explain to me the final part , that would be great thanks....

Please help (Headbang)