MatricesHard

Question

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

Options

A.If detA = ± 1, then A-1 exists but all its entries are not necessarily integers
B.If detA ≠ ± 1, then A-1 exists and all its entries are non-integers
C.If detA = ± 1, then A-1 exiexists and all its entries are integers
D.If detA = ± 1, then A-1 need not exist

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 = (adj A)
⇒     all entries in A-1 are integers.

Create a free account to view solution

View Solution Free
Topic: Matrices·Practice all Matrices questions

More Matrices Questions

Let A, B & C are three matrices such thatA = , B = , C = If there exist three real numbers x, y, z (not all zero simulta...If A = and B = (adj A), and C = 5A, then is equal to-...If order of A + B is n × n, then the order of AB is -...If A = and n ∈ N, then An is equal to-...If the matrices A, B, (A + B) are non-singular (where A and B are of same order), then (A(A+B)-1B)-1 is equal to -...