$A$ is of order 2 × 3 and $B$ is of order 3 × 4. What is the order of $(AB)'$?

Explanation

1. 01

   $AB$ is defined because $A$ has 3 columns and $B$ has 3 rows; $AB$ is 2 × 4.

2. 02

   The transpose swaps rows and columns, so $(AB)'$ is 4 × 2.