  The semileptonic decays and two-body nonleptonic decays of light baryon octet
($T_8$) and decuplet ($T_{10}$) consisting of light $u,d,s$ quarks are studied
with the SU(3) flavor symmetry in this work. We obtain the amplitude relations
between different decay modes by the SU(3) irreducible representation approach,
and then predict relevant branching ratios by present experimental data within
$1 \sigma$ error. We find that the predictions for all branching ratios except
$\mathcal{B}(\Xi\rightarrow \Lambda^0\pi)$ and $\mathcal{B}(\Xi^*\rightarrow
\Xi\pi)$ are in good agreement with present experimental data, that implies the
neglected $C_+$ terms or SU(3) breaking effects might contribute at the order
of a few percent in $\Xi\rightarrow \Lambda^0\pi$ and $\Xi^*\rightarrow \Xi\pi$
weak decays. We predict that $\mathcal{B}(\Xi^{-}\rightarrow
\Sigma^0\mu^-\bar{\nu}_\mu)=(1.13\pm0.08)\times10^{-6}$,
$\mathcal{B}(\Xi^{-}\rightarrow\Lambda^0\mu^-\bar{\nu}_\mu)=(1.58\pm0.04)\times10^{-4}$,
$\mathcal{B}(\Omega^-\rightarrow\Xi^0\mu^-\bar{\nu}_\mu)=(3.7\pm1.8)\times10^{-3}$,
$\mathcal{B}(\Sigma^-\rightarrow
\Sigma^0e^-\bar{\nu}_e)=(1.35\pm0.28)\times10^{-10}$,
$\mathcal{B}(\Xi^-\rightarrow \Xi^0e^-\bar{\nu}_e)=(4.2\pm2.4)\times10^{-10}$.
We also study $T_{10}\to T_8 P_8$ weak, electromagnetic or strong decays. Some
of these decay modes could be observed by the BESIII, LHCb and other
experiments in the near future. Due to the very small life times of $\Sigma^0$,
$\Xi^{*0,-}$, $\Sigma^{*0,-}$ and $\Delta^{0,-}$, the branching ratios of these
baryon weak decays are only at the order of $\mathcal{O}(10^{-20}-10^{-13}$),
which are too small to be reached by current experiments. Furthermore, the
longitudinal branching ratios of $T_{8A} \to T_{8B} \ell^-
\bar{\nu}_\ell~(\ell=\mu,e)$ decays are also given.
