Consider the following grammars $($S is the start symbol$)$

G$1$: S $$ A B G$2$: S $$ A $|$ B G$3$: S $$ A B

A $$ B A $$ A $$

A $$ B $$ B $$

B $$

Which of the following is true?

only G$2$ is ambiguous

G$1$ and G$3$ are ambiguous

G$2$ and G$3$ are ambiguous

G$1$ and G$2$ are ambiguous

only G$3$ is ambiguous