Prove the (S U(3)) results in Eq. (5.3.29): (mathbf{3} otimes overline{mathbf{3}}=mathbf{8} oplus mathbf{1} ; mathbf{3} otimes mathbf{3}=mathbf{6}

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Prove the \(S U(3)\) results in Eq. (5.3.29): \(\mathbf{3} \otimes \overline{\mathbf{3}}=\mathbf{8} \oplus \mathbf{1} ; \mathbf{3} \otimes \mathbf{3}=\mathbf{6} \oplus \overline{\mathbf{3}} ; \mathbf{8} \otimes \mathbf{3}=\mathbf{1 5} \oplus \overline{\mathbf{6}} \oplus \mathbf{3}\); and \(\mathbf{3} \otimes \mathbf{3} \otimes \mathbf{3}=\mathbf{1 0} \oplus \mathbf{8} \oplus \mathbf{8} \oplus \mathbf{1}\).

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