reserve i,n for Nat,
  K for Field,
  M1,M2,M3,M4 for Matrix of n,K;

theorem Th28:
  n>0 implies 0.(K,n)<>1.(K,n)
proof
A1: Indices (1.(K,n))=[:Seg n,Seg n:] by MATRIX_0:24;
  assume n>0;
  then n >=0+1 by INT_1:7;
  then 1 in Seg n;
  then
A2: [1,1] in [:Seg n, Seg n:] by ZFMISC_1:87;
  assume
A3: 0.(K,n)=1.(K,n);
  Indices (0.(K,n))=Indices (1.(K,n)) by MATRIX_0:26;
  then (0.(K,n))*(1,1)=0.K by A2,A1,MATRIX_1:1;
  then 0.K=1.K by A2,A3,A1,MATRIX_1:def 3;
  hence contradiction;
end;
