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  1. Aug 2021
    1. Show that the product of two unitary matrices UUU and VVV is also unitary.

      I would go as follows (spoiler alert, try to solve this by yourself first!): $$(UV)^\dagger=V^\dagger U^\dagger$$ Then we can use the definition of unitary matrix: $$UV\cdot(UV)^\dagger = U\underbrace{VV^\dagger}_I U^\dagger = UU^\dagger = I$$