 Hi and welcome to the session. Let's work out the following question. The question says, using the properties of determinant, evaluate the following. That is, i is equal to the determinant 0ab2ac2a2b0bc2a2ccb20. Let's start with the solution to this question. We have the determinant i as 0ab2ac2a2b0bc2a2ccb20. Now, taking out a2, b2 and c2, common from first column, second column and third column respectively. So taking a2, b2, c2 from column 1, column 2 and column 3, respectively we get a2 into b2 into c2 into determinant 0aab0bcc0. Now, taking out a, b and c from r1, r2 and r3 respectively, we get a2, b2, c2 into aabc into determinant 01110110. This is equal to aq, bq, cq. Now here we operate column 2 goes to column 2 minus column 3. So we have determinant 011. Now 1 minus 1 is 0, 0 minus 1 is minus 1, 1 minus 0 is 1, 1, 1, 0. Now, expanding from the first row, we get aq, bq, cq into 1 into 1 plus 1. That is equal to aq into bq into cq into 2 and that is equal to 2aq, bq, cq. So this is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day.