State true or false and give appropriate proof $($if claiming true$)$ or counter$-$example $($if claiming false$).$

Let A $=\{$a$1,...,$ an$\}$ and C $=\{$c$1,...,$ cn$\}.$ If a$1$ prefers c$1$ the most and c$1$ also prefers a$1$ the most, Then any stable matching must match a$1$ to c$1.$