  We report measurements of B to pseudoscalar-pseudoscalar decays with at least
one eta meson in the final state using 140 fb^{-1} of data collected by the
Belle detector at KEKB e^+ e^- collider. We observe the decay B^+-> eta pi^+
and find evidence of B^+-> eta K+; the measured branching fractions are B(B^+->
eta pi^+)=(4.8^{+0.8}_{-0.7}(stat) +- 0.3(sys))*10^{-6} and B(B^+-> eta
K^+)=(2.1 +- 0.6(stat)+- 0.2(sys))*10^{-6}. Their corresponding CP violating
asymmetries are measured to be 0.07+- 0.15 (stat) +- 0.03(sys) for eta pi^+-
and -0.49+- 0.31 (stat) +- 0.07(sys) for eta K^+-. No significant signals are
found for neutral B->eta h decays. We report the following upper limits on
branching fractions at the 90% confidence level: B(B-> eta K^0 < 2.0* 10^{-6},
B(B-> eta pi0)<2.5*10^{-6} and B(B-> eta eta) <2.0*10^{-6}.
