Find the submatrix with the smallest mean, 2.0
Mathematica, 77 50 bytes

±x_:=x~Subsets~{3}
Min[Mean/@Mean/@±#&amp;/@±#]&amp;


 is Mathematica's transposition operator (and is rendered as a superscript T in Mathematica).

This answer first defines a helper operator ± which returns all 3-element subsets of a list, and then evaluates to an unnamed function which uses this operator to solve the problem.

This is done by first computing all 3-element subsets of the matrix's rows. Then for each such subset, we transpose it and compute its 3-element subset of rows. This gives us all possible 3x3 submatrices (although they are transposed). We then compute the mean on all of them and find the overall minimum.