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

JEE 2008
A

If `detA = +-1,` then `A^(-1)` exists but all its entries are not necessarily integers

B

If `detA != +-1,` then `A^(-1)` exists and all its entries are non-integers

C

If `detA = +-1,` then `A^(-1)` exists and all its entries are integers

D

If `detA = +-1`, `then A^(-1)` need not exist

HINT

`A^(-1) = 1/(det(A)) (adj. A)`

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