  We study the \egg, \egm and \epg decays using an extended three-flavor
Nambu-Jona-Lasinio model that includes the 't~Hooft instanton induced
interaction. We find that the $\eta$-meson mass, the \egg, \egm and \epg decay
widths are in good agreement with the experimental values when the $U_{A}(1)$
breaking is strong and the flavor $SU(3)$ singlet-octet mixing angle $\theta$
is about zero. The calculated $\eta \gamma \gamma^\ast$ transition form factor
has somewhat weaker dependence on the squared four-momentum of the virtual
photon. The effects of the $U_A(1)$ anomaly on the scalar quark contents in the
nucleon, the $\Sigma_{\pi N}$ and $\Sigma_{KN}$ terms and the baryon number one
and two systems are also studied.
