Question

Let A be (2n+1)×(2n+1) matrix with integer entries and positive determinant,where n∈N.If AAT = I = ATA, then which of the following statements always holds?

• A. det(A)=0
• B. det(A+I)≠0
• C. det(A+I)=0
• D. det(A-I)=0
• E. det(A-I)≠0

Answer 1

Answer: (D)

det(A-I)=0

Answer 2

The correct option is (D): det(A-I)=0