 Hello and welcome to the session, I am Deepika here. Let's discuss the question by using properties of determinants show that determinant 1 plus a square minus b square 2ab minus 2b 2ab 1 minus a square plus b square 2b minus 2a 1 minus a square minus b square is equal to 1 plus a square plus b square whole cube. Let's start the solution. We have on the left hand side as this is equal to 1 plus a square minus b square 2ab 2b 2ab 1 minus a square plus b square minus 2a minus 2b 2a 1 minus a square minus b square. By applying c1 goes to c1 minus bc3 and c2 goes to c2 plus ac3 we get our left hand side is equal to now c1 goes to c1 minus bc3. This is equal to 1 plus a square minus b square plus 2b square this is equal to 1 plus a square plus b square. Now 2ab minus 2ab this is equal to 0 again 2b minus b plus a square b plus b cube. This is equal to b we can take it common and 1 plus a square plus b square. Now c2 goes to c2 plus ac3 so here we get 2ab minus 2ab this is equal to 0 1 minus a square plus b square plus 2a square. This is equal to 1 plus a square plus b square again minus 2a plus a minus a cube minus a b square this is equal to minus a into 1 plus a square plus b square. c3 is as it is minus 2b 2a 1 minus a square minus b square. We can take 1 plus a square plus b square common from c1 as well as from c2 so by taking out factor 1 plus a square plus b square common from c1 and c2 we get our left hand side is equal to 1 plus a square plus b square into 1 plus a square plus b square. Now here in c1 we get 1 0b in c2 we get 0 1 minus a and c3 is as it is. Now by applying 3 goes to r3 minus br1 we get our left hand side is equal to 1 plus a square plus b square whole square into 1 0 minus 2b 0 1 2a. Now r3 goes to r3 minus br1 that is b minus b is equal to 0 minus a 1 minus a square minus b square plus 2b square this is equal to 1 minus a square plus b square. This is equal to 1 plus a square plus b square whole square now by expanding along c1 we get 1 into 1 into 1 minus a square plus b square that is 1 minus a square plus b square minus minus of 2a square that is plus 2a square by expanding along. This is equal to 1 plus a square plus b square whole square into 1 plus a square plus b square which is equal to 1 plus a square plus b square whole cube this is our right hand side. Hence our left hand side is equal to right hand side. I hope the question is clear to you. Bye and have a good day.