function B = Tij(A,i,j)
[m,n] = size(A);
B = zeros(m,n);
% case 1
B(i,j) = 1/A(i,j);
% case 2
for k = [1:i-1 i+1:m]
　　B(k,j) = -1*A(k,j)/A(i,j);
end
% case 3
for k = [1:j-1 j+1:n]
　　B(i,k) = A(i,k)/A(i,j);
end
% case 4
for k = [1:i-1 i+1:m]
　　for s = [1:j-1 j+1:n]
　　　　B(k,s) = A(k,s) - A(k,j)*A(i,s)/A(i,j);
　　end
end
end

function B = inv_by_Tij(A)
[~,n] = size(A);
B = zeros(n);
C = 1:n;
L = zeros(1,n);
for i = 1:n
　　[~,j] = max(A(i,C));
　　A = Tij(A,i,C(j));
　　L(i) = C(j);
　　C(C==C(j)) = [];
end
for i = 1:n
　　for j = 1:n
　　　　B(L(i),j) = A(i,L(j));
　　end
end
end