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 / ii / Solution

Left multiplication by $E$ interchanges rows three and four; applying it twice restores every row. Equivalently, it sends the standard basis vectors $e_3,e_4$ to each other and fixes $e_1,e_2$, so its square fixes a basis. $E^2=I$.