Question

If $A$ is a $3\times 3$ nonsingular matrix and if $|A|=3$, then $|(2A{)}^{-1}|$= _______

• A. $\frac{1}{3}$
• B. $\frac{1}{24}$
• C. $24$
• D. $3$

Answer 1

Answer: (B)

Given, $|A{|}_{3\times 3}\ne 0$ and $|A|=3$
Then, $\left|(2A{)}^{-1}\right|=\left|\frac{1}{2A}\right|=\frac{1}{|2A|}$
$=\frac{1}{(2{)}^3}\cdot \frac{1}{|A|}\left(\because |aA|=a^3|A|\right)$
$=\frac{1}{8}\cdot \frac{1}{3}=\frac{1}{24}$