Two $2 \times 2$ square matrices $A , B$ satisfy
$$A B + A ^ { 2 } B = E , \quad ( A - E ) ^ { 2 } + B ^ { 2 } = O$$
Among the statements in the following, which are correct? (Here, $E$ is the identity matrix and $O$ is the zero matrix.) [4 points]
\textbf{Statements}\\
ᄀ. The inverse matrix of $B$ exists.\\
ㄴ. $A B = B A$\\
ㄷ. $\left( A ^ { 3 } - A \right) ^ { 2 } + E = O$\\
(1) ㄴ\\
(2) ㄷ\\
(3) ᄀ, ㄴ\\
(4) ᄀ, ㄷ\\
(5) ᄀ, ㄴ, ㄷ