$F$ is a field iff $F$ is a Principal Ideal Domain

A commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain.

I have done the part that if $F$ is a field then $F[x]$ is a PID using the division algorithm and contradicting the minimality of degree of a polynomial.

But I am facing difficulty to do the other part.

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