Question

If $A$ and $B$ are square matrices of order $3$ such that $\left|A\right|=-1,\left|B\right|=3$, then $\left|3AB\right|=$

• A. $-9$
• B. $-81$
• C. $-27$
• D. $81$

Answer 1

The correct option is B $-81$

Since, we know that $|KA|=K^n|A|$ if $A$ is of order $n$.
Given, $A$ and $B$ both are of order $3$.
$\therefore AB$ is also of order $3$.
$\Rightarrow |3AB|=3^3|AB|=27|A||B|$ [$\because |AB|=|A||B|$]
$=27(-1)\left(3\right)$
$=-81$
Option $B$ is correct.