  Dimensional reduction of the D=2 minimal super Yang-Mills to the D=1 matrix
quantum mechanics is shown to double the number of dynamical supersymmetries,
from N=1 to N=2. We analyze the most general supersymmetric deformations of the
latter, in order to construct the noncritical 3D M-theory matrix model on
generic supersymmetric backgrounds. It amounts to adding quadratic and linear
potentials with arbitrary time dependent coefficients, namely, a cosmological
`constant,' Lambda(t), and an electric flux background, rho(t), respectively.
The resulting matrix model enjoys, irrespective of Lambda(t) and rho(t), two
dynamical supersymmetries which further reveal three hidden so(1,2) symmetries.
All together they form the supersymmetry algebra, osp(1|2,R). Each so(1,2)
multiplet in the Hilbert space visualizes a dynamics constrained on either
Euclidean or Minkowskian dS_{2}/AdS_{2} space, depending on its Casimir. In
particular, all the unitary multiplets have the Euclidean dS_{2}/AdS_{2}
geometry. We argue that the matrix model provides holographic duals to the 2D
superstring theories on various backgrounds having the spacetime signature
Minkowskian if Lambda(t)>0, or Euclidean if Lambda(t)<0.
