Hi Community,

I am working on a tutorial for matrix algebra, I cannot figure out how to make Mathematica identify and replace previously defined symbols in calculations. For example. I have defined

rules = {IdentityMatrix[2] -> Subscript[\[Sigma], 0], 
  PauliMatrix[1] -> Subscript[\[Sigma], 1], 
  PauliMatrix[2] -> Subscript[\[Sigma], 2], 
  PauliMatrix[3] -> Subscript[\[Sigma], 3]}

So when I make

Grid[Join[{Table[PauliMatrix[i] // MatrixForm, {i, 3}]}, 
  Table[MatrixForm[PauliMatrix[i].PauliMatrix[j] /. rules], {i, 
    3}, {j, 3}]]]

I get Subscript[\[Sigma], 0] in the diagonal, but cannot figure out how I make Mathematica to identify the other elements as simply products of +/- I and the other Pauli matrices.

Or simpler put: how do I make Mathematica answer I PauliMatrix[3] to the input

PauliMatrix[1].PauliMatrix[2]

Kind regards

Mogens

Ps. Is it true that Solve etc. does not work on matrices, or is it just me? (I have tried to specify Matrices[{2,2},Complexes] as the domain but I get errors or nothing back)