There will be three more days of hearings by the committee looking into financial irregularities at Ornge, which is also the subject of a criminal probe by provincial police.
Matthews has already testified, but much of what she told the committee was contradicted by former Ornge CEO Chris Mazza during an emotional appearance last week.
Both the Conservatives and New Democrats say they want Matthews to help clear up some of the contradictory testimony.
Matthews painted a picture of a rogue organization that was stonewalling government officials about a complex web of for-profit spin off companies set up at Ornge.
But Mazza insisted the health ministry always knew about changes he was making and never told him he had veered off course.
The committee also tried to recall Mazza for this week's sessions, but his doctors have sent a letter saying he is medically unfit to testify.
Two Speaker's warrants had to be issued to force Mazza's original appearance, but the committee can't meet again until the legislature resumes in the fall so he won't be facing questions this week.