Question

Let A be a matrix of order 3 × 3 such that det(A) = 2, B = 2A^-1 and $C=\frac{(adjA)}{\sqrt[3]{16}}$ , then the value of det(A³B²C³) is

Answer 1

Answer: 2

$\left|A\right|=2,\left|B\right|=\left|2A^{-1}\right|=\frac{2^3}{|A|}=2^2$
$\left|C\right|=\left|\frac{adjA}{\sqrt[3]{16}}\right|=\frac{1}{16}\cdot 2^2=\frac{1}{2^2}$
$\therefore det.\left(A^3{B}^2{C}^3\right)=2^3\cdot {\left(2^2\right)}^2\cdot {\left(\frac{1}{2^2}\right)}^3=2$