$3\times3$ matrix

Algebra Level 3

Fill in the blank:

Let $A$ be a $3\times3$ matrix and $|A|=8.$

Then the value of $|(6A)^{-1}|$ is $\text{ \_\_\_\_\_}.$

\dfrac{1}{1728}

\dfrac{1}{56}

\dfrac{1}{1264}

\dfrac{1}{48}

1 solution

Nazmus Sakib
Sep 25, 2017

$|(6A)^{-1}|$

$=6^{-3} \dot\ |A|^{-1}$

$=\dfrac{1}{216} \times\dfrac{1}{A}$

$=\dfrac{1}{216} \times\dfrac{1}{8}$

$=\dfrac{1}{1728}$