Change of basis and product in associative algebra

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Hello,

I have a finite dimensional algebra over rationals, defined by multiplication matrices. I am using

B = FiniteDimensionalAlgebra(QQ, [R,ME23,ME13,ME12,MDe1,MDe2,MDe3,ME1,ME2,ME3,MD1,MD2,MD3,Md])

for some matrices like

R=Matrix([r,E23,E13,E12,De1,De2,De3,E1,E2,E3,D1,D2,D3,d])

and lists

r=[1,0,0,0,0,0,0,0,0,0,0,0,0,0]

to define the algebra.

What I need is a the coefficient of some products with respect to a new basis, more precisely: I have an explicit basis of the form $H_1:= E12+E,H_2\dots$ and I would like to find the coefficients of $H_i*H_j$ with respect to the new basis. Is there a specific command to get this?

I have a problem already in computing

B(H1)*B(H2)

indeed they say that H1 has not the expected length.

Thanks a lot in advance!