Comment #2 on issue 2231 by [email protected]: Matrix determinant properties are not satisfied.
http://code.google.com/p/sympy/issues/detail?id=2231

What version of SymPy do you use? In master branch of our development repository your example gives:

In [1]: var('a,b,c,d')
Out[1]: (a, b, c, d)

In [2]: B=Matrix([a,b],[c,d])
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/home/mateusz/repo/git/sympy/<ipython console> in <module>()

/home/mateusz/repo/git/sympy/sympy/matrices/matrices.pyc in __init__(self, *args)
    154             self.mat = []
    155         else:
--> 156             raise TypeError("Data type not understood")
    157
    158     def key2ij(self,key):

TypeError: Data type not understood

Also don't compare expressions like this

 Matrix.det(B)*Matrix.det(B) == Matrix.det(B*B)

because `==` is structural comparison operator, e.g.

In [5]: a*(a + b) == a**2 + a*b
Out[5]: False

Correct would be to write:

In [6]: (B**2).det() == expand(B.det()**2)
Out[6]: True

Compare this with:

In [7]: (B**2).det() == B.det()**2
Out[7]: False

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