 Hi and welcome to the session I am the Picker here. Let's discuss a question. The question says, by using properties of determinants, show that determinant 0A-B-A0-C B-C0 is equal to 0. Let's start the solution. Let delta is equal to or given determinant 0A-B-A0-C B-C0. By using the properties of determinant, we have to prove that delta is equal to 0. This can be written as delta is equal to minus 1 into minus 1 into minus 1 take minus 1 common from each row. We get 0 minus A-B-A0-C minus B-C0. That is by taking minus 1 common from each row. By interchanging R-I to C-I, we get delta is equal to minus 1 into 0 minus A-B. Second row is interchanging to second column A-0-C and third row is interchanging to third column minus B-C0. Just see that this is our delta. Therefore delta is equal to minus 1 into delta from the question. This implies delta is equal to minus delta. Again, this implies delta plus delta is equal to 0, which implies 2 delta is equal to 0. This implies delta is equal to 0, which implies 0 minus A-B-A0-C minus B-C0 is equal to 0, hence proved. I hope the question is clear to you. Bye and have a good day.