The biggest rocket ever made launched from the company's Starbase launchpad in Boca Chica, Texas for Starship Flight 6 ... in a test to see if both stages of the spacecraft -- the Super Heavy booster and the Starship capsule -- would return safely back to Earth ... and Trump had a front-row seat.

After blasting off and travelling into space, the Super Heavy booster essentially flew in reverse back to Earth -- it was supposed to be "grabbed" by the launch and catch tower's "chopstick" arms, but it instead landed in the Gulf of Mexico. A couple minutes into the mission, SpaceX had announced a "no go" for the attempted booster catch. The booster was meant to be reusable, but won't be since it landed in saltwater, which it's not designed to withstand.

Meanwhile, the Starship capsule -- which was sent into space by the Super Heavy booster, and will be used to ferry astronauts to the moon, and ultimately Mars, according to Musk -- made a successful controlled descent into the Indian Ocean.

While orbiting the Earth, the Starship capsule successfully reignited one of its Raptor engines ... a first for the mission.

Elon has polarized folks in this country with his involvement in American politics ... backing Trump and then bringing the President-elect to Tuesday's launch ... but there's no denying Musk runs a company with some pretty ingenious innovations.