One problem related to power train driveline has been reported for the 2005 Toyota Matrix. The most recently reported issues are listed below.
My 2005 Toyota Matrix 4wd started to making whining noise at 69000 miles. Took the car to nearby mechanic and found that the rear differential unit needs to be replaced. The differential fluid was fully-replaced at 50,000 miles and the car has been properly maintained accordingly by manufacture's guidance. The cost is more than $ 1500 to replace rear differential. . For any car equipped with awd system should never have this issue and I fee that it's very unsafe to drive.