I've been following this discussion with interest and have wondered how the ITA Matrix works. As I understand it, Google Flights is a sub-set of the Matrix application with one significant feature (usually) added.... a fairly direct mechanism to access and purchase the fares without the assistance of a travel agent or one or more airline agents.
My specific interest is a trip from Ottawa to Auckland with a return from Sydney for next year. I will be able to purchase this without problem from Air Canada and/or United and, as you might guess, spend a king's ransom on business class.
So, my question is: if I can identify an itinerary in ITA Matrix at a favourable price with all the coding provided, what can I do with that?