What is wrong with this Gauss-Pivoting algorithm?

Goodevening everyone,

My name's Antonio and I'm from Italy. I am currently doing some projects in MATLAB, and there's this easy one giving me some problems. The algorithm is about resolving a linear system using Gauss and partial pivoting.

      % initializing the permutation vector 
      for i = 1:n
          piv(i) = i;
      end
  % using Gauss
      for k = 1:(n-1)

          [maximum, max_position] = max(abs(A(piv(k:n), k)));
          if maximum <= eps*norm(A)
              error('Pivot is too small.')
          end
          if A(piv(max_position), k) ~= 0
              if piv(max_position) ~= k
                  piv([k piv(max_position)]) = piv([piv(max_position) k]);
              end
              for i = (k+1):n
                  A(piv(i), k) = A(piv(i), k)/A(piv(k), k);
                  for j = (k+1):n
                      A(piv(i), j) = A(piv(i), j)-[A(piv(i), k)*A(piv(k), j)];
                  end
                  b(piv(i)) = b(piv(i)) - A(piv(i), k)*b(piv(k));
              end
          else
              error('singular')
          end
      end
      if A(piv(n), n) == 0
          error('singular')
      end

      x(n) = b(piv(n))/A(piv(n), n);
      for i = (n-1):-1:1
          sum = 0;
          for k = (i+1):n
              sum = sum + A(piv(i), k)*x(k);
          end
          x(i) = (b(piv(i)) - sum)/A(piv(i), i);
      end
     end

This is the code. But when i try it with this script, the solution of the systems, which should be [1, ..., 1], is wrong.

clear num = input('Inserire la massima dimensione delle matrici di prova: ');

for k = 1:100
    A = rand(k);
    x = ones(k, 1);
    b = A*x;
    x = GaussPivoting(A, b)
end

any idea of what could be the problem?

Thank you in advance