Question

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

• A. $3^{n^2+1}$
• B. $2^{n^2+1}\cdot 5$
• C. $3^{n^2}\cdot 2$
• D. $3^{n^3}$

Answer 1

The correct option is C $3^{n^2}\cdot 2$

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