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Question: symbolic operations with arbitrary matrices

Question:symbolic operations with arbitrary matrices

chandr 15 Maple 13
matrix symbol
August 06 2012
2

Hi all! 
Is there any possibility in Maple to perform symbolic operations with arbitrary matrices (possibly given only the size of the matrix or it's structure (block matrices, diagonal matrix and so on)). For example, I would like to obtain the following results (input -> output). 

Possible code: 

assume(A, Matrix(n)): assume(B, Matrix): assume(E,IdentityMatrix(n)): 

expand((A.B)^(-1)); -> B^(-1).A^(-1) 
expand((A^2.B)'); -> B'.(A')^2 # A' is transpose 
factor(B.A+A); -> (B+E).A 
combine(A^(-1).B^(-1).C^(-2)); -> (C^2.B.A)^(-1) 

and so on. 

Thank you. 
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