
Defining function
Hi,
I have matrixes A={{1,1}},B={{z, 0}, {0, z}} and C=Transpose[A]. After multiplying A.B.C I get expected result {{2z}}. Furthermore I tried to define function f[z_]:=A.B.C and plot graph of this function like Plot[f[a],{a,1,2}]. Now I did not get expected result, the linear function, but I got empty plot. Where I do a mistake? Help me, please.

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)