I have a washer in the basement, the drain pipe is a one inch steel pipe that ties into the 6 inch cast iron main about 5 or 6 inches above the washer. The house is about 50 years old and the inspector said I have to put a p trap into the washer drain. Since the pipe is already above the washer where should the p trap be installed and how could I tie it into a one inch line without cutting a bigger hole in the main. Could a check valve be used in this case instead of a p trap to achieve the same results?

Without a trap between the washer and the sewer you have a direct open connection between the sewer and your house. If a "P" trap's installed you will also need a vent otherwise you would be building a outlawed "S" trap.
I'm surprised the inspector didn't inform you about the vent. A one inch drain line has just got to be giving you problems and a check valve does not substitute for a trap. Good luck, Tom