Or HaChaim on Leviticus 9:7/אור החיים על ויקרא ט׳:ז׳

1 וכפר בעדך ובעד העם. "and make atonement for yourself and for the people." We learn from this that Aaron's own atonement effected the atonement of the people. This is because Aaron's sin was brought about through the Israelites. Had they not demanded from Aaron that he make a deity for them, none of all this would have happened. As long as Aaron had not obtained atonement for his part in that sin, both the sinner and the one who had been the prime cause of that sin still remained guilty. As soon as Aaron obtained atonement, so did the people. We derive all this from the linkage of the two atonements in this verse i.e. "on your behalf and on behalf of the people."