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 \[A=\pm 1\], then \[{{A}^{-1}}\] exists but all its entries are not necessarily integers
D) If det \[A=\pm 1\], then \[{{A}^{-1}}\] exists and all its entries are non-integers
Correct Answer: A
Solution :
Obviously (a) is the correct answer.
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