From the value of A we may separate those members which contain a particular element a ik as a factor, and write the portion aik A ik; A k, the **cofactor** of ar k, is called a minor of order n - i of the determinant.

Hence anAu = auk t a22a33...ann, where the **cofactor** of an is clearly the determinant obtained by erasing the first row and the first column.

A ll a33 ï¿½ï¿½ï¿½ a32 a33 ï¿½ï¿½ï¿½ a3n an2 an3 ï¿½ï¿½ï¿½ ann Similarly A ik, the **cofactor** of aik, is shown to be the product of (-) i+k and the determinant obtained by erasing from A the ith row and k th column.