#### Question

Using the property of determinants and without expanding, prove that:

`|(a-b,b-c,c-a),(b-c,c-a,a-b),(a-a,a-b,b-c)| = 0`

#### Solution

Here, the two rows R_{1} and R_{3} are identical.

Δ = 0.

Is there an error in this question or solution?

Solution Using the Property of Determinants and Without Expanding, Prove that |(A-b,B-c,C-a),(B-c,C-a,A-b),(A-a,A-b,B-c)| = 0 Concept: Properties of Determinants.