Question

If A and B are square matrices of second order such that $|A|=-1,|B|=3$, then what is $|3AB|$ equal to?

• A. $3$
• B. $-9$
• C. $-27$
• D. None of the above

Answer 1

Answer: (C)

$-27$

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

$3\left|AB\right|\left|kA\right|=k^2\left|A\right|$

$={\left(3\right)}^2\left|A\right|\left|B\right|$

$={\left(3\right)}^2(-1)\left(3\right)=-27$

Option C