Manipal MET2011MathematicsMatrices
Let A be a square matrix all of whose entries are integers. Then, which one of the following is true?
Options
- AIf det (A)= 1 , then A⁻¹ exists but all its entries are not necessarily integers
- BIf det (A) 1 , then A⁻¹ exists and all its entries are non-integers
- CIf det (A) = 1 , then A⁻¹ exists and all its entries are integers
- DIf det (A)= 1 , then A⁻¹ need not exist
Correct answer
C. If det (A) = 1 , then A⁻¹ exists and all its entries are integers
Step-by-step solution
As det (A)= 1, A⁻¹ exists and A⁻¹= 1 det (A) ( adj A)= adj A All entries in adj (A) are integers. A⁻¹ has integer entries.