Comment #7 on issue 3691 by mrock...@gmail.com: Add determinant to matrix expressions
http://code.google.com/p/sympy/issues/detail?id=3691

SymPy has two kinds of matrix objects.  Explicit ones

x = Matrix(2, 2, [1, 2, 3, 4])
2*x
[2, 4]
[6, 8]

and purely symbolic ones

x = MatrixSymbol('X', 2, 2)
2*x
2*X

The second case we call matrix expressions. They don't actually compute results, they just represent computations that could be done. I recommend that you look at the current implementation of Trace
https://github.com/sympy/sympy/blob/master/sympy/matrices/expressions/trace.py

You could copy it (and it's associated test file in tests/test_trace.py) and make very small modifications. You shouldn't worry about the `doit` method to start. Once that is in place it will be easier to talk about next steps like what asmeurer mentioned above.

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