product between symmetric matrix and transpose matrix

Question

Suppose that B is a symmetric matrix and A generic matrix with $A^T$ its transpose, is it true that:

$B*A = B*A^T $ ?

i think that $B*A = (B^T)*(A^T) = B*(A^T) $ so is true

And if A,B were 2 tensors?

Answer 1

No it is false because $B=I $ is a symmetric matrix but for all non-symmetric matrix $A$ you have that

$A=I*A\neq I* A^t$