Question

$\left| \begin{matrix} a + b & b + c & c + a \\ b + c & c + a & a + b \\ c + a & a + b & b + c \end{matrix} \right| = K\left| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \end{matrix} \right|,$ then $K =$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B)

2

Answer 2

The determinant can be written sum of $2 \times 2 \times 2 = 8$ determinants of which 6 are reduces to zero because of their two rows are identical. Hence proceed.