For two matrices $A = \left( \begin{array} { l l } 1 & 1 \\ 0 & 1 \end{array} \right) , B = \left( \begin{array} { l l } 1 & 0 \\ 1 & 1 \end{array} \right)$, define sets $S , T$ as $$\begin{aligned}
& S = \left\{ \binom { x } { y } \left\lvert \, \binom { x } { y } = A ^ { n } \binom { 1 } { 1 } \right. , n \text { is a natural number} \right\} \\
& T = \left\{ \binom { x } { y } \left\lvert \, \binom { x } { y } = B ^ { n } \binom { 1 } { 1 } \right. , n \text { is a natural number} \right\}
\end{aligned}$$ Which of the following in are correct? [4 points] 〈Remarks〉 ㄱ. If $\binom { a } { b } \in S$, then $\binom { b } { a } \in T$. ㄴ. If $\binom { a } { b } \in S , \binom { c } { d } \in S$, then $\binom { a + c } { b + d } \in S$. ㄷ. If $\binom { a } { b } \in S , \binom { p } { q } \in T$, then the matrix $\left( \begin{array} { l l } a & p \\ b & q \end{array} \right)$ has an inverse matrix. (1) ㄱ (2) ㄱ, ㄴ (3) ㄱ, ㄷ (4) ㄴ, ㄷ (5) ㄱ, ㄴ, ㄷ
For two matrices $A = \left( \begin{array} { l l } 1 & 1 \\ 0 & 1 \end{array} \right) , B = \left( \begin{array} { l l } 1 & 0 \\ 1 & 1 \end{array} \right)$, define sets $S , T$ as
$$\begin{aligned}
& S = \left\{ \binom { x } { y } \left\lvert \, \binom { x } { y } = A ^ { n } \binom { 1 } { 1 } \right. , n \text { is a natural number} \right\} \\
& T = \left\{ \binom { x } { y } \left\lvert \, \binom { x } { y } = B ^ { n } \binom { 1 } { 1 } \right. , n \text { is a natural number} \right\}
\end{aligned}$$
Which of the following in <Remarks> are correct? [4 points]\\
\textbf{〈Remarks〉}\\
ㄱ. If $\binom { a } { b } \in S$, then $\binom { b } { a } \in T$.\\
ㄴ. If $\binom { a } { b } \in S , \binom { c } { d } \in S$, then $\binom { a + c } { b + d } \in S$.\\
ㄷ. If $\binom { a } { b } \in S , \binom { p } { q } \in T$, then the matrix $\left( \begin{array} { l l } a & p \\ b & q \end{array} \right)$ has an inverse matrix.\\
(1) ㄱ\\
(2) ㄱ, ㄴ\\
(3) ㄱ, ㄷ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ