 Hi and welcome to the session. I am Deepika here. Let's discuss a question. Question says, by using properties of determinants, prove that determinant minus a square a b a c b a minus b square b c c a c b and minus c square is equal to 4 a square b square c square. Let's start the solution. On left hand side we have minus a square b a c a a b minus b square c b a c b c and minus c square a b c minus a b c a minus b c a b minus c. By taking a b c common from r 1 r 2 r 3 respectively we get this. It is by taking a b c common in r 1 r 2 and r 3 respectively which is equal to a b c square minus 1 1 1 by taking a common from column 1 and 1 minus 1 1 by taking b common and 1 1 minus 1. That is by taking a b c common in c 1 c 2 and c 3 respectively. By applying r 1 goes to r 1 plus r 2 and r 2 goes to r 2 plus r 3 we get left hand side is equal to a b c square 0 0 1 1 minus 1 which is equal to a square b square c square 0 minus 0 plus 2 into 2 1 0 1 by expanding along first row which is equal to a square b square c square into 2 into 2 which is equal to 4 a square b square c square which is equal to r right hand side left hand side is equal to right hand side. I hope the question is clear to you.