first of all, A.B.C is "the matrix" {{2z}}, and Mathematica doesn't know how to build graphs of matrices. if you write (A.B.C)[[1,1]] you'll be getting 2z (this [[1,1]] says that you're taking the (1,1)-st element of that "matrix")

second of all, instead of f[z_]:=(A.B.C)[[1,1]], write it as f[z_]=(A.B.C)[[1,1]] and you should be good (I'm sure not why it doesn't build the plot when you write it with := but sometimes it behaves like that)