Two $2 \times 2$ square matrices $A , B$ satisfy
$$2 A ^ { 2 } + A B = E , \quad A B + B A = 2 A + E$$
Which of the following statements are correct? Choose all that apply from <Remarks>. (Given that $E$ is the identity matrix.) [4 points]
\section*{<Remarks>}
ㄱ. $A ^ { - 1 } = 2 A + B$\\
ㄴ. $B = 2 A + 2 E$\\
ㄷ. $( B - E ) ^ { 2 } = O$ (where $O$ is the zero matrix.)\\
(1) ㄴ\\
(2) ㄷ\\
(3) ㄱ, ㄴ\\
(4) ㄱ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ