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

theorem Th43:
  for n being Nat, A being Matrix of n,K holds Det A = Det (A@)
proof
  let n be Nat, A be Matrix of n,K;
  n=0 or n>=1 & n is Nat by NAT_1:14;
  then Det A=1_K & Det A@=1_K or Det A = Det A@ by Th41,MATRIX_7:37;
  hence thesis;
end;
