  We study string interactions in the fermionic formulation of the c=1 matrix
model. We give a precise nonperturbative description of the rolling tachyon
state in the matrix model, and discuss S-matrix elements of the c=1 string. As
a first step to study string interactions, we compute the interaction of two
decaying D0-branes in terms of free fermions. This computation is compared with
the string theory cylinder diagram using the rolling tachyon ZZ boundary
states.
