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Symbolic matrix operations


Does anyone know how to perform symbolic matrix operations in mathematica 
without computing on the element level?
For example, if I need to expand (AB)^T and get the result in the form B^T 
A^T, what should I type?
I am trying to find a way to simplify matrix equations without actually 
multiplying, transposing, inversing etc matrices on the element level.

Thanks.
DS



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