Let A be a square matrix all of whose entries are integers.
Let A be a square matrix all of whose entries are integers. Then which one of the following is true?
(a) If det A = ± 1, then A–1 need not exist
(b) If det A = ± 1, then A–1 exists but all its entries are not necessarily integers
(c) If det A ≠ ± 1, then A–1 exists and all its entries are nonintegers
(d) If det A = ± 1, then A–1 exists and all its entries are integers
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(d) : Each entry of A is an integer, so the cofactor of every entry is an integer. And then each entry of adjoint is integer.
Also det A = ± 1 and we know that
A-1 = (adj A) /detA
This means all entries in A–1 are integers.
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