Iran did invade Iraq.

Check your facts.

The war was initiated by Iraq launching an air and land invasion of Iraq, without any warning, ultimatum or declaration of war. After this attack was repulsed Iranian forces counterattacked and occupied Iraqi territory until the end of the war (which ended soon after the US shot down a civilian Iranian airliner, which was taken by the Iranians as an indication that the USA was at the point of moving in in support of Saddam Hussein's Iraqi regime). After the war Iran withdrew to the prewar boundaries.