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So suppose $f_{ijk}$ is the antisymmetric structure constant of SU(3), and $D^8_{ij}(g)$ is the matrices of 8-dimensional adjoint representation of SU(3), then how to show that $f_{ijk}$=$D^8_{il}(g)$$D^8_{jm}(g)$$D^8_{kn}(g)$$f_{lmn}$ which shows that the structure constant is indeed invariant.

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