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Based on a sample of $1.31 \times 10^9$ $J/\psi$ events collected with theBESIII detector at the BEPCII collider, Dalitz plot analyses of selected 79,625$\eta\rightarrow\pi^{+}\pi^{-}\pi^0$ events, 33,908$\eta\rightarrow\pi^0\pi^0\pi^0$ events and 1,888$\eta^{\prime}\rightarrow\pi^0\pi^0\pi^0$ events are performed. The measuredmatrix elements of $\eta\rightarrow\pi^+\pi^-\pi^0$ are in reasonable agreementwith previous measurements. The Dalitz plot slope parameters of$\eta\rightarrow\pi^0\pi^0\pi^0$ and $\eta^{\prime}\rightarrow\pi^0\pi^0\pi^0$are determined to be $-0.055 \pm 0.014 \pm 0.004$ and $-0.640 \pm 0.046 \pm0.047$, respectively, where the first uncertainties are statistical and thesecond systematic. Both values are consistent with previous measurements, whilethe precision of the latter one is improved by a factor of three. Final stateinteractions are found to have an important role in those decays.

Measurement of the Matrix Elements for the Decays $\eta \rightarrow \pi^{+}\pi^{-}\pi^0$ and $\eta/\eta^{\prime}\rightarrow\pi^0\pi^0\pi^0$