JEE Math Practice Question

Let $$A$$ be a square matrix all of whose entries are integers. Then which one of the following is true?

1. A.If det $$A = \pm 1,$$ then $${A^{ - 1}}$$ exists but all its entries are not necessarily integers
2. B.If det $$A \ne \pm 1,$$ then $${A^{ - 1}}$$ exists and all its entries are non integers
3. C.If det $$A = \pm 1,$$ then $${A^{ - 1}}$$ exists but all its entries are integers
4. D.If det $$A = \pm 1,$$ then $${A^{ - 1}}$$ need not exists