Question

If a, b, c be positive and not all equal, then the value of the determinant $\left| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \end{matrix} \right|$ is –

• A. +ive
• B. –ive
• C. Depends on a, b, c
• D. None

Answer 1

Answer: (B)

–ive

Answer 2

short trick put a = 1, b = 2, c = 3

$\left| \begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2 \end{matrix} \right|$ = 1(5) – 2(1)(1) + 3(–7) = 5 – 2 – 21 = – ive