Question

If $AandB$ are square matrices of order $3$ such that $\left|A\right|=–1,\left|B\right|=3,$ then $\left|3AB\right|$ is equal to

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

Answer 1

The correct option is B

$–81$

Explanation for correct option:

It is given that:

$\left|A\right|=-1;\left|B\right|=3$

$\begin{array}{rcl}\left|3AB\right|& =& 3^3\left|AB\right|\\ & =& 27\left|AB\right|\\ & =& 27\left|A\right|\left|B\right|\\ & =& 27\times 3\times (-1)\\ & =& -81\end{array}$

Hence, the correct answer is option (B).