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Yes, the $S_3$ permutation action on $A = \{x_1, x_2, x_3\}$ is faithful because its kernel is $\{1\}$, the singleton containing only the identity element.

Conditions: $G = S_3$, the symmetric group of degree 3.; $A = \{x_1, x_2, x_3\}$.; The action is defined by $\sigma x_i = x_{\sigma(i)}$.

Yes, the $S_3$ permutation action on $A = \{x_1, x_2, x_3\}$ is faithful because its kernel is $\{1\}$, the singleton containing only the identity element.

Conditions: $G = S_3$, the symmetric group of degree 3.; $A = \{x_1, x_2, x_3\}$.; The action is defined by $\sigma x_i = x_{\sigma(i)}$.

A group action is called faithful when its kernel is exactly the singleton set containing only the identity element of $G$, i.e., $\{g \mid ga = a\} = \{1\}$.

Conditions: The action has a kernel as defined in the video.; $\{1\}$ denotes the singleton containing the identity element of $G$.

A group action is called faithful when its kernel is exactly the singleton set containing only the identity element of $G$, i.e., $\{g \mid ga = a\} = \{1\}$.

Conditions: The action has a kernel as defined in the video.; $\{1\}$ denotes the singleton containing the identity element of $G$.