Which word describes a strongly ingrained habit or behavior?

The term that describes a strongly ingrained habit or behavior is "inveterate." This word specifically refers to something that has been established for a long time, often implying a negative connotation, indicating a habit or practice that is difficult to change. For example, an inveterate smoker is someone who has smoked for many years and finds it challenging to quit due to the long-standing nature of the habit.

The choice of "invincible" refers to something incapable of being conquered or overcome, which does not pertain to habits or behaviors. "Inhibited" describes a state of being restrained or held back, often in a social context, and is unrelated to the notion of ingrained habits. "Indeterminate" refers to something that is not clearly defined or established, which is contrary to the idea of a well-defined, ingrained habit. Thus, "inveterate" is the term that accurately captures the essence of a long-standing and firmly established behavior.