Question

If $\left| \begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix} \right|$ = 5, then the value of

$\left| \begin{matrix} b_{2}c_{3}–b_{3}c_{2} & a_{3}c_{2}–a_{2}c_{3} & a_{2}b_{3}–a_{3}b_{2} \\ b_{3}c_{1}–b_{1}c_{3} & a_{1}c_{3}–a_{3}c_{1} & a_{3}b_{1}–a_{1}b_{3} \\ b_{1}c_{2}–b_{2}c_{1} & a_{2}c_{1}–a_{1}c_{2} & a_{1}b_{2}–a_{2}b_{1} \end{matrix} \right|$is –

• A. 5
• B. 25
• C. 125
• D. 0

Answer 1

Answer: (B)

25

Answer 2

D = 5(given), D' = ? But D' = D^n–1 Ž D^3–1 = D² = (5)² = 25