theorem Th28:
  AutMt(id V1,b1,b1) = 1.(K,len b1)
proof
  set A=AutMt(id V1,b1,b1);
  set ONE=1.(K,len b1);
A1: len A=len b1 by MATRIX_0:def 2;
A2: now
    let i such that
A3: 1<=i & i<=len b1;
A4: i in dom b1 by A3,FINSEQ_3:25;
A5: i in Seg len b1 by A3;
    i in dom A by A1,A3,FINSEQ_3:25;
    hence A.i = A/.i by PARTFUN1:def 6
      .= ((id V1).(b1/.i)) |-- b1 by A4,MATRLIN:def 8
      .= (b1/.i) |-- b1
      .= Line(ONE,i) by A4,Th19
      .= ONE.i by A5,MATRIX_0:52;
  end;
  len ONE=len b1 by MATRIX_0:def 2;
  hence thesis by A1,A2;
end;
