Answer is less clear. US was hesitant to go above the 38th parallel line once N Korean army was routed. They were happy to stop there and go back to having 38th

Answer is less clear. US was hesitant to go above the 38th parallel line once N Korean army was routed. They were happy to stop there and go back to having 38th parallel line before the Korean War started. However the S Korean troops just marched across 38th parallel in order to reunite the peninsula under 1 government. And the US troops in away just kept going with them. Because the Korean war was so unexpected, no thoughts had been given on what to do. The Korean peninsula had been 1 kingdom for over 500 years, far longer than Germany as a nation. Both N Korea and S Korean leaders had been calling for a united Korea, even with force, even before the Korean War. For this reason, US govt hesitated giving heavy weapons to S Korea before the start of the Korean War. So no, US didn't exactly invade N Korea. N Korea invaded S Korea first.