In The Iliad, does Achilles know that he has been dipped in the River Styx and that he is invincible except for the spot on his heel?

The various legends concerning Achilles' invulnerability
are wildly contradictory. The most famous relates to his mother, Thetis, dipping him
into the River Styx but failing to fully submerge the heel by which she held him--thus,
the Achilles heel legend. Other tales relate that Thetis bathed her son in ambrosia and
then burned him with fire--also creating an invulnerable state. Other stories, including
Homer's The Iliad, mention that Achilles was wounded more than once
in battle, which would seem to rebuke the invulnerability aspect entirely. In any case,
there seems to be no mention that Thetis told her son of this special condition, and
Achilles' ferocity in battle appears to be due to his boldness--not because of a
knowledge of his own invulnerability.