$A$ is a square matrix of order 3 with $|A| = 2$. What is $|3A^{-1}|$?

Explanation

1. 01

   $|kB| = k^{n}|B|$ for order $n$, and $|A^{-1}| = \frac{1}{|A|}$.

2. 02

   $|3A^{-1}| = 3^{3} \times \frac{1}{2} = \frac{27}{2}$.