Question

If $A$ and $B$ are square matrices of order $n,$ such that $|A|=2$ and $|B|=1,$ then the value of $|2A||3B|$ is

• A. $3^n\cdot 2$
• B. $6^n\cdot 2$
• C. $2^{n+1}$
• D. $6^{n+1}$

Answer 1

The correct option is B $6^n\cdot 2$

Given $|A|=2$ and $|B|=1$
$\Rightarrow |2A||3B|=2^n|A|\cdot 3^n|B|$
$(\therefore |KA|=K^n|A|,\text{where}n\text{is the order of}A)$
$\Rightarrow |2A||3B|=6^n|A||B|$
$\Rightarrow 6^n|A||B|=6^n\cdot 2\cdot 1=6^n\cdot 2$