If
A={{1,0,0},{0,0,0},{0,0,0}}
B={{a,b,c},{d,e,f},{g,h,i}}
then your first matrix is A x B and your second matrix is B x A, where "x" means tensor product. I'm not sure if new versions of Mathematica have the "tensor product" implemented, I already use an old code made by myself for that.