$A$ and $B$ are square matrices of order 3 with $|A| = 2$ and $|B| = -3$. What is $|2AB|$?

Explanation

1. 01

   $|AB| = |A||B| = -6$.

2. 02

   $2AB$ is a 3 × 3 matrix times 2, so $|2AB| = 2^3|AB| = 8(-6) = -48$.