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

Q: JEE Main 2018 Matrices & Determinants: Let be a square matrix all of whose entries are integers. Then which one of the following is true?...

The correct answer is A. As all entries of square matrix are integers, therefore all co-factors should also be integers. If det then exists. Also all entries of are integers.

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As all entries of square matrix are integers, therefore all co-factors should also be integers. If det then exists. Also all entries of are integers.

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If det then exists but all its entries are not necessarily integers

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If det then exists and all its entries are non integers

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If det then exists but all its entries are integers

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If det then need not exists

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