Question:-
Option (A)
If detA = ± 1, then A^{–1} exists but all its entries are not necessarily integers
Option (B)
If detA ≠ ± 1, then A^{–1} exists and all its entries are non-integers
Option (C)
If detA = ± 1, then A^{–1} exists and all its entries are integers
Option (D)
If detA = ± 1, then A^{–1} need not exist
Correct Option:
C
Question Solution:
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.