We report a $^{71}$Ga nuclear-quadrupole-resonance (NQR) study on the characteristics of superconductivity in noncentrosymmetric Ir$_2$Ga$_9$ at zero field (H=0). The $^{71}$Ga-NQR measurements have revealed that $1/T_1$ has the clear coherence peak just below $T_{rm c}$, and decreases exponentially upon further cooling in Ir$_2$Ga$_9$. From these results, Ir$_2$Ga$_9$ is concluded to be the conventional s-wave superconductor. Despite the lack of spatial centrosymmetry, there are no evidence for unconventional superconducting state ascribed to ASOC in Ir$_2$Ga$_9$.
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