reserve x for set,
  D for non empty set,
  k,n,m,i,j,l for Nat,
  K for Field;

theorem Th46:
  for A,B being Matrix of n,REAL holds Det (A*B) = (Det A)*(Det B)
proof
  set K=F_Real;
  let A,B be Matrix of n,REAL;
  reconsider Na=MXR2MXF A, Nb=MXR2MXF B as Matrix of n,K;
  Det (A*B) = (Det Na) * (Det Nb) by Th45
    .= (Det A)*(Det B);
  hence thesis;
end;
