Algebraic topology – Class space loop space

Leave $ U (n) $ be the unit group $ n $-matrices My question is why we have the following isomorphism.

$$ Omega BU (n) simeq U (n) $$

where $ BU (n) = E / U (n) $ is the classifying space and $ Omega BU (n) = Hom (S ^ 1, BU (n)) $ denotes the space of the loop.

Is $ Omega BU (n) simeq U (n) $ above also a $ H $-equivalence (therefore iso of $ H $-spaces)?