Demonstrate that for colors \(r, g\), and \(b\), color \(\mathrm{SU}(3)\) two-quark states are of the form \(q q=\mathbf{3} \otimes \mathbf{3}=\mathbf{6} \oplus \overline{\mathbf{3}}\), with

Show that this implies that the non-color part of any two-quark wavefunction in a baryon must be symmetric.

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3 (antisymmetric) = (rg - gr,rb- br, bg -gb), 6 (symmetric)=(rg + gr, rb + br, gb + bg, rr, gg, bb).