  We consider a solution of a IKKT-type matrix model which can be considered as
a 1+1-dimensional space-time with Minkowski signature and a Big Bounce-like
singularity. A suitable $i\varepsilon$ regularization of the Lorentzian matrix
integral is proposed, which leads to the standard $i\varepsilon$-prescription
for the effective field theory. In particular, the Feynman propagator is
recovered locally for late times. This demonstrates that a causal structure and
time evolution can emerge in the matrix model, even on non-trivial geometries.
We also consider the propagation of modes through the Big Bounce, and observe
an interesting correlation between the post-BB and pre-BB sheets, which
reflects the structure of the brane in target space.
