  Using simple algebraic methods along with an analogy to the BFSS model, we
explore the possible (target) spacetime symmetries that may appear in a matrix
description of de Sitter gravity. Such symmetry groups could arise in two ways,
one from an ``IMF'' like construction and the other from a ``DLCQ'' like
construction. In contrast to the flat space case, we show that the two
constructions will lead to different groups, i.e. the Newton-Hooke group and
the inhomogeneous Euclidean group (or its algebraic cousins). It is argued that
matrix quantum mechanics based on the former symmetries look more plausible.
Then, after giving a detailed description of the relevant one particle
dynamics, a concrete Newton-Hooke matrix model is proposed. The model naturally
incorporates issues such as holography, UV-IR relations, and fuzziness, for
gravity in $dS_{4}$. We also provide evidence to support a possible phase
transition. The lower temperature phase, which corresponds to gravity in the
perturbative regime, has a Hilbert space of infinite dimension. In the higher
temperature phase where the perturbation theory breaks down, the dimension of
the Hilbert space may become finite.
