Question 1 of 35

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

If det (A) = ± 1, then A^-1 exists but all its entries are not necessarily integers

If det (A) ≠ ± 1, then A^-1 exists and all its entries are non-integers

If det (A) = ± 1, then A^-1 exists and all its entries are integers

If det (A) = ± 1, then A^-1 need not exist