Question

Write the value of `|(a-b, b- c, c-a),(b-c, c-a, a-b),(c-a, a-b, b-c)|`

Answer 1

Let Δ = `|(a-b, b- c, c-a),(b-c, c-a, a-b),(c-a, a-b, b-c)|`   

By R₁ → R₁ + R₂ + R₃

⇒ Δ = `|(0, 0, 0),(b-c, c-a, a-b),(c-a, a-b, b-c)|` = 0  ...(as all elements of R₁ are zero).