Let A be (2 n+1) \times(2 n+1) matrix with integer entries and positive determinant. Where n \in \mathbb{N}. If A A_{-}^T=I=A^T A then which of the following statements always holds ?

Correct Answer is : det(A−I)=0

KEAM 2023 Math Solved Paper

Question : 9 of 120

Marks: +1, -0

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

det(A)=0
det(A+I)≠0
det(A+I)=0
det(A−I)=0
det(A−I)≠0

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