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matrices & polynomials in mathematica


I have the following problem.
I have written a mathematica-module that automatically produces a certain
polynomial as a result. But I want another module to use this first module
and fill in a matrix in this polynomial.
for example: f[x]=1+x+x^2
But when I compute f[A] where A is a matrix, mathematica interprets 1 as a
matrix filled with ones in stead of the identity-matrix. And A^2 is
pointswise multiplication in stead of matrix-multiplication.
Is there an option to let Mathematica know that the polynomial works on


PS. I am aware of the possibility to multiply matrices using . (dot) but the
problem is that the polynomial is the result of some computations and I need
to have mathematica interpret this polynomial on matrices automatically.

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