Assume the basis vectors of the fundamental representation for color \(\mathrm{SU}(3)\) to correspond to the "colors" \(r, g\), and \(b\). Write the properly symmetrized wavefunction corresponding to a singlet color \(\mathrm{SU}(3)\) state. Show that if a gluon \(G\) transforms as the adjoint \(\mathrm{SU}(3)_{\mathrm{c}}\) representation, both \(G G\) and \(G G G\) have a 1 in their \(\mathrm{SU}(3)\) irrep content; thus, particles of this composition (glueballs) might exist in nature.