Let $F$ be a certain field.
Prove or disprove that the following statements:
The equation $X^3=0_F$ has only one solution.
The equation $X^3=1_F$ has only one solution.
Suppose F is finite, then the equation $X^3=1_F$ has only one solution.
I'm pretty sure all of them are true but I'm not sure how to write the proof so any help would be appreciated.
Note: I'm only in my first few weeks of linear algebra so I don't think any advanced solutions would help.