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[tex]U(|a \rangle \otimes |b \rangle)[/tex]

is U distributive over the tensor product or does it behave like the dot product with scalars, i.e.

[tex]U(|a \rangle \otimes |b \rangle) = U|a \rangle \otimes |b \rangle = |a \rangle \otimes U|b \rangle [/tex]