Question

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

Answer 1

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