If a, b and c are negative and different real numbers, then = | array lll a & b & c b & c & a c & a & b array | is

Step-by-step solution

Given, = | array lll a & b & c b & c & a c & a & b array | Applying, C₁ C₁+C₂+C₃ and taking common from C₁ aligned & =(a+b+c) | array lll 1 & b & c 1 & c & a 1 & a & b array | & =-(a+b+c) [a^2+b^2+c^2-a b-b c-c a ] & =- (a+b+c) 2 [(a-b)^2+(b-c)^2+(c-a)^2 ] & 0 as a, b, c 0 aligned