pivot and inverse

B = [2 8 -1;5 -1 1;-1 1 4];
n =length(B);
E = [B eye(n)];
D=zeros(n);
for i = 1 : n-1
    [m,id]=max(abs(E(i:end,i)))
    id=id+i-1;
    if(id~=i)
         temp=E(i,:);
        E(i,:)=E(id,:);
        E(id,:)=temp;
    end
    for j = i+1 :  n
        E(j,:)=E(j,:)-(E(i,:)*E(j,i))/E(i,i)
    end
end

% x = zeros(1,n);
% for i = n:-1:1
%     x(i) = (E(i,end) - (sum(E(i,1:end-1).*x)))/E(i,i);
% end

for i = n:-1:2
    [m,id]=max(abs(E(i:end,i)))
    id=id+i-1;
    if(id~=i)
         temp=E(i,:);
        E(i,:)=E(id,:);
        E(id,:)=temp;
    end
    for j = i-1:-1:1
        E(j,:)=E(j,:)-(E(i,:)*E(j,i))/E(i,i);
    end
end
for i =  1 : n
    E(i,:)=E(i,:)/E(i,i)
end


for i = 1 : n
    D(i,:)=E(i,n+1:end)
end