It is WRONG (=very ineffective) way to calculate this determinant using co-factor method.


You can get the answer MUCH FASTER and with minimum calculations (actually, without massive calculations) using properties of determinant.



a)  Replace the second row of the matrix by the sum of the first and the second rows of the given matrix.


    Then the second row becomes  (5, 5, 5, 5).


    Determinant of the transformed matrix will be the same as for the original matrix, by the fundamental property of the determinant.




b)  Next, replace the fourth row of the matrix by the sum of the third and the fourth rows of the given matrix.


    Then the fourth row becomes  (5, 5, 5, 5).


    Determinant of the transformed matrix will be the same as for the original matrix, by the fundamental property of the determinant.




c)  Now the transformed matrix contains two identical rows, the second and the fourth, consisting of four "5",  (5,5,5,5).


    Hence, due to the other fundamental property, the determinant of the transformed matrix is zero.


    Therefore, the determinant of the original matrix is equal to 0 (zero, ZERO).