Question

If $|A|=2$, $|B|=1$ and order of matrix is $3\times 3$ then value of $|adjAB|$ is

• A. 4
• B. 2
• C. 16
• D. 64

Answer 1

Answer: (A)

4

The order of matrix $A$ is $3\times 3$ and the order of matrix $B$ is $3\times 3$

So the order of matrix $AB$ is $3\times 3$

$\Rightarrow |adjAB|=|AB{|}^{(3-1)}=|AB{|}^2=|A{|}^2|B{|}^2$

Given $|A|=2$ and $|B|=1$

$\Rightarrow |adjAB|=|A{|}^2|B{|}^2=4$

Therefore the correct option is $A$