If detA = ± 1, then A–1 exists but all its entries are not necessarily integers
If detA ≠ ± 1, then A–1 exists and all its entries are non-integers
If detA = ± 1, then A–1 exists and all its entries are integers
If detA = ± 1, then A–1 need not exist
Each entry of A is integer, so the cofactor of every entry is an integer and hence each entry in the
adjoint of matrix A is integer.
Now detA = ± 1 and A-1 = 1/det(A)(adj A)
Þ all entries in A-1 are integers.