Matrices with parameters

I believe the matrix has to be defined over a polynomial ring. For example, the code

> R<x> := PolynomialRing(Integers());
> M := Matrix(R,2,2,[[x,2],[3,x-1]]);
[    x     2]
[    3 x - 1]

You can compute with this thing too. For example,

> Determinant(M);
x^2−x−6

If you then wanted to change the base ring to, say $\mathbb{Q}[x]$, we proceed as follows:

> S<x> := PolynomialRing(Rationals());
> N := ChangeRing(M,S);