theorem Th35:
  Det M <> 0.K implies M~ = (Det M)" * (Matrix_of_Cofactor M)@
proof
  set C=(Det M)" * (Matrix_of_Cofactor M)@;
  assume
A1: Det M <> 0.K;
  then
A2: M*C=1.(K,n) by Th30;
  C*M=1.(K,n) by A1,Th33;
  then
A3: M is_reverse_of C by A2,MATRIX_6:def 2;
  M is invertible by A1,Th34;
  hence thesis by A3,MATRIX_6:def 4;
end;
