theorem Th49:
  Det <*N*> = <*Det N*>
proof
  set F=<*N*>;
A1: len F=1 by FINSEQ_1:40;
A2: n=len N by MATRIX_0:def 2;
A4: len F=len (Det F) by CARD_1:def 7;
A5: dom (Det F)=Seg len F by FINSEQ_2:124;
  1 in Seg 1;
  then (Det F).1=Det (F.1) by A1,A5,Def7;
  hence thesis by A1,A4,A2,FINSEQ_1:40;
end;
