matrix expression simplify [closed]

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i am wondering if it is possible to simplify:

T*V + V*T // V = V^(t) symmetric

where both operands are matrixes

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I don't think this is possible due to the following considerations:

If we multiply two matrices A and T, where A is symmetric (i.e. A(i,j) = A(j,i)), we have the following:

For A*T we have that the item in row z and column s is computed as:

 __n__
 \
 /     A(z,i)*T(i,s)
 -----
  i=1

For the other way around, T*A, we get for row z, column s:

 __n__                     __n__
 \                         \
 /     T(z,i)*A(i,s)  =    /     T(z,i)*A(s,i)
 -----                     -----
  i=1                       i=1

So, as long as we do not know anything about the entries T(i,j) in T, I think we can not say how these sums relate to each other.