Question

Let A be the matrix of order $3\times 3$ such that $|A|=1,$ $B=2A^{-1}$ and $C=\frac{\left(adjA\right)}{\sqrt[3]{32}}$, then the value of $|A{B}^2.C^3|$ is
[Note : |A| represent determinant value of matrix A.]

Answer 1

$|A|=1$

$adj\left(A\right)=|A{|}^{n-1}=1^{3-1}=1$

$A^{-1}=\frac{adj\left(A\right)}{|A|}$

$=\frac{1}{1}=1$

$B=2A^{-1}=2\times 1=2$

$C=\frac{adj\left(A\right)}{\sqrt[3]{32}}=\frac{1}{\sqrt[3]{32}}$

$\therefore |A{B}^2{C}^3|=1\times 2^2\times \frac{1}{2}=2$