The Basics of Judaism: Sin and Repentance: The Immortality of Adam:
Was Adam immortal until he sinned?
The Tree of Life wasn't explicitly forbidden to Adam (see Gen. 2:16-17),
but according to Gen. 3:22, after Adam ate from the Tree of Knowledge
of Good and Evil, G-d expelled him from the Garden to ensure that he
wouldn't also eat from the Tree of Life and live forever; this
implies that since he never ate from it, he was never immortal.
Ask a follow-up question
