Conformal Killing and Ricci collineation equations for (2+1)-dimensional Friedmann-Robertson-Walker (FRW) spacetimes are solved. These spacetimes are classified according to their Ricci conformal collineations (RCCs) and Ricci collineations (RCs). In the non-degenerate and degenerate cases of the Ricci tensor (the cases det(R-ab) not equal 0 and det(R-ab) = 0, respectively), the general forms of the vector fields generating RCCs and RCS are obtained. When the Ricci tensor is degenerate, the special cases are classified and it is shown that there are many cases of RCCs and RCs with infinite degrees of freedom. Furthermore, it is found that when the Ricci tensor is non-degenerate, the groups of RCCs and RCs are finite-dimensional, and we have always 10-parameter group of RCCs and 6-parameter group of RCs which are the maximal possible dimension for three-dimensional spacetime manifold. The results obtained are compared with conformal Killing vectors and Killing vectors.