  First passage of stochastic processes under resetting has recently been an
active research topic in the field of statistical physics. However, most of
previous studies mainly focused on the systems with continuous time and space.
In this paper, we study the effect of stochastic resetting on first passage
properties of discrete-time absorbing Markov chains, described by a transition
matrix $\brm{Q}$ between transient states and a transition matrix $\brm{R}$
from transient states to absorbing states. Using a renewal approach, we exactly
derive the unconditional mean first passage time (MFPT) to either of absorbing
states, the splitting probability the and conditional MFPT to each absorbing
state. All the quantities can be expressed in terms of a deformed fundamental
matrix $\brm{Z_{\gamma}}=\left[\brm{I}-(1-\gamma) \brm{Q} \right]^{-1}$ and
$\brm{R}$, where $\brm{I}$ is the identity matrix, and $\gamma$ is the
resetting probability at each time step. We further show a sufficient condition
under which the unconditional MPFT can be optimized by stochastic resetting.
Finally, we apply our results to two concrete examples: symmetric random walks
on one-dimensional lattices with absorbing boundaries and voter model on
complete graphs.
