%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-05-18 20:58:57
 % @LastEditTime: 2021-05-18 21:27:03
 % A : [9, m]
%--------------------------
function invA = inv_3rank(A)
    detA = det_3rank(A); % 1,m

    indicator = [(-1)^(1+1), (-1)^(1+2), (-1)^(1+3); 
                (-1)^(1+2), (-1)^(2+2), (-1)^(3+2);
                (-1)^(1+3), (-1)^(2+3), (-1)^(3+3);];
    indicator = indicator(:); % 9,1

    M11 = A(5,:) .* A(9,:) - A(6,:) .* A(8,:);
    M12 = A(4,:) .* A(9,:) - A(6,:) .* A(7,:);
    M13 = A(4,:) .* A(8,:) - A(5,:) .* A(7,:);
    M21 = A(2,:) .* A(9,:) - A(3,:) .* A(8,:);
    M22 = A(1,:) .* A(9,:) - A(3,:) .* A(7,:);
    M23 = A(1,:) .* A(8,:) - A(2,:) .* A(7,:);
    M31 = A(2,:) .* A(6,:) - A(3,:) .* A(5,:);
    M32 = A(1,:) .* A(6,:) - A(3,:) .* A(4,:);
    M33 = A(5,:) .* A(1,:) - A(2,:) .* A(4,:);

    M = [M11; M12; M13; M21; M22; M23; M31; M32; M33];
    
    invA = detA .* (indicator .* M);
end
% 1,4,7
% 2,5,8
% 3,6,9