If ring $B$ is integral over $A$, then an element of $A$ which is a unit in $B$ is also a unit in $A$.
Solution 1:
Hint: If
$$x^{-n}+a_{n-1}x^{-n+1}+\cdots+a_1 x^{-1}+a_0=0$$
Then
$$x^{-1}+a_{n-1}+\cdots+a_1x^{n-2}+a_0x^{n-1}=0$$
If ring $B$ is integral over $A$, then an element of $A$ which is a unit in $B$ is also a unit in $A$.
Solution 1:
Hint: If
$$x^{-n}+a_{n-1}x^{-n+1}+\cdots+a_1 x^{-1}+a_0=0$$
Then
$$x^{-1}+a_{n-1}+\cdots+a_1x^{n-2}+a_0x^{n-1}=0$$