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

Options

A. if det `A = pm 1 ` , then `A^(-1)` need not exist
B. If det `A = pm 1 , ` then `A^(-1)` exists but all its entries are necessarily integers
C. If det `A != pm 1` then `A^(-1)` exists and all its entries are non - integers
D. If det `A = pm 1 ` , then `A^(-1) ` exists and all its entries are integers .

Answer

D