On Q(a,b,c,d)

We may work with symbolic matrices:

> C:=matrix(2,2,[a,b,3*c,d]): B:=matrix(2,2,[a,b,5*c,d]): A:=diag(C,B);

[Maple Math]

> FROBENIUS(A);

[Maple Math]

Asking for the change basis matrix

Testing the output