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

Question

( A ) If det$A = \pm 1, then A^{–1}$ exists and all its entries are integers
( B ) If det$A =\pm 1, then A^{–1}$ need not exist
( C ) If det$A \neq\pm 1, then A^{–1}$ exists and all its entries are non-integers
( D ) If det$A = \pm 1, then A^{-1}$ exists but all its entries are not necessarily integers