Solution
= Solution
The $j$th column of $AE$ is $A(Ee_j)$. The <permutation matrix> fixes $e_1,e_2$ and interchanges $e_3,e_4$, so these columns are $Ae_1,Ae_2,Ae_4,Ae_3$. They are exactly the first, second, fourth and third columns of $A$. Thus \b[right multiplication by $E$ interchanges columns three and four], leaving the others unchanged.