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Let $R_1$ and $R_2$ be integral domains.

Which of the following is true of $R_1 \times R_2$

$R_1 \times R_2$ is also an integral domain.

If $R_1$ or $R_2$ is a field, then $R_1 \times R_2$ is an integral domain.

If both $R_1$ and $R_2$ are fields, then $R_1 \times R_2$ is an integral domain.

$R_1 \times R_2$ is never an integral domain.