Question

Let $A$ and $B$ be two $3\times 3$ matrices such that $AB=I$ and $|A|=\frac{1}{8}$ then $|\text{adj}(\text{Badj}(2A))|$ is equal to

• A. 16
• B. 32
• C. 64
• D. 128

Answer 1

Answer: (C)

$AB=i$
$|\text{adj}(B$ adj $(2A)|=|B$ adj ${(2A)|}^2$
$=|B{|}^2$ |adj ${(2A)|}^2$
$=|B{|}^2{\left(|2A{|}^2\right)}^2=|B{|}^2{\left(2^6|A{|}^2\right)}^2$
$|A|=\frac{1}{8}$ and $|AB|=1\Rightarrow |A||B|=1$
$\Rightarrow \frac{1}{8}|B|=1$
$\Rightarrow |B|=8$
required value $=64$