 Hello and welcome to the session. Today we will discuss the following question which says find the co-factor of A12 in the following that is the determinant of order 3 by 3 with any means 2 minus 3, 5, 6, 0, 4, 1, 5, minus 7. Before moving on to the solution let's learn how to find out the co-factor of an element. Co-factor of an element say Aij denoted as Aij is given by minus 1 raised to the power i plus j into Mij where Mij is the minor of the element Aij. So for this we also need to know what is the minor of Aij. The minor of Aij is the determinant obtained by deleting the ith row and jth column in which the element Aij rise. This is the key idea for this question. Now let's see its solution. We are given the determinant of order 3 by 3 with elements 2 minus 3, 5, 6, 0, 4, 1, 5, minus 7. We need to find out the co-factor of A12 that is the element which lies in the first row and second column. So here this is the A12 element. Now first of all let us find out the minor of the element A12 which is given by M12. Now we will get M12 by deleting the first row and the second column of the given determinant. So here we are left with these four elements. Thus minor of the element A12 that is M12 is the determinant of order 2 by 2 with elements 6, 4, 1, minus 7 which will be equal to 6 into minus 7 minus 1 into 4 that is minus 42 minus 4 which is equal to minus 46. Now the co-factor of the element A12 denoted by A12 will be equal to minus 1 raised to the power 1 plus 2 into M12 which will be equal to minus 1 raised to the power 3 into minus 4 is 6 which is M12. So this will be equal to 46. Thus the co-factor of the element A12 is 46. So this is the required answer to this question. With this we finish this session. Hope you must have enjoyed it. Goodbye, take care and have a nice day.