 Hello and welcome to the session. I am Deepika here. Let's discuss a question using the property of determinants and without Expanding prove that determinant a minus b, b minus c, c minus a, b minus c, c minus a, a minus b C minus a, a minus b, b minus c is equal to 0 Let's start the solution Solution, here delta is equal to our given determinant That is a minus b, b minus c, c minus a, b minus c, c minus a, a minus b C minus a, a minus b, b minus c. We have to prove that delta is equal to 0 Now by applying R1 goes to R1 plus R2 Plus R3 to delta We get we get delta is equal to now a minus b Plus b minus c plus c minus a because we are applying R1 goes to R1 plus R2 plus R3 again b minus c plus c minus a plus a minus b and This is c minus a plus a minus b plus b minus c and the second row is as it is b minus c, c minus a, a minus b and This is c minus a, her row is also as it is a minus b, b minus c Now on cancellation we get delta is equal to first row is 0 0 0 This is b minus c, c minus a, a minus b, c minus a, a minus b, b minus c Since all elements of R1 are 0 therefore delta is equal to 0, R1 are 0 therefore delta is equal to 0, hence proved. We have proved that our given determinant is equal to 0. I Hope the question is clear to you. Bye and have a good day