% The derminant of a matrix can be evaluated using a recursive formula such
% that: Assuming a square matrix A of order n
% det(A)=sum(a1j*Cj), for j=1,n
% where a1j represent the elements of the 1st row of the matrix A, and
% Cj is the determinant of the reduced matrix obtained removing the 1st row
% and the column j of the matrix A
function DetA=determin(A)

% This method can be applied for any nxn square matrix; 

% Check Input Argument
if isempty(A)
    error('cof:EmptyMatrix','The matrix A does not exist');
end

[r, c]=size(A);     % number of rows and columns of A
if r~=c
    error('det:NotSquareMatrix','The matrix A is not square');
end

DetA=0;

% Calculate determinant
if r==2,
%     if the matrix a 2x2 matrix, then directly calculate the determinant
%     using the common formula
    DetA=A(1,1)*A(2,2)-A(1,2)*A(2,1);
else
%     if the matrix is not 2x2 reduce its order of 1, generating a matrix
%     with r-1 rows and c-1 columns. Subsequently recall the function using
%     the reduced matrix
    temp_A=A;
    for i=1:c
        a1i=temp_A(1,i);    % save the element of the 1st row and ith column of the temporary matrix; this element will be used to calculate the determinant later on
        if a1i~=0
            temp_A(1,:)=[];     % remove the first row to create the reduced matrix
            temp_A(:,i)=[];     % remove the ith column to create the reduced matrix
            Cj=temp_A;
            DetCj=determin(Cj); % Calculate the determinant of the reduced matrix recalling the function
            DetA=DetA+((-1)^(1+i))*a1i*DetCj;
            temp_A=A;           % reset elements of temporary matrix to input elemens
        end
    end
end