Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Digital systems, linear algebra, introduction to formal proof / 5 / b / iv / Solution

The $j$th column of $AE$ is $A(E{e}_j)$. The permutation matrix fixes $e_1,e_2$ and interchanges $e_3,e_4$, so these columns are $A{e}_1,A{e}_2,A{e}_4,A{e}_3$. They are exactly the first, second, fourth and third columns of $A$. Thus right multiplication by $E$ interchanges columns three and four, leaving the others unchanged.