Updates:
        Status: Invalid

Comment #3 on issue 2231 by asmeurer: Matrix determinant properties are not satisfied.
http://code.google.com/p/sympy/issues/detail?id=2231

Yes, the correct way to compare expressions is to canonize them with expand or some other function. An even better way to test equality is to subtract one from the other and see if you can reduce it to 0, like

simplify((B**2).det() - B.det()**2)
0

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