Answer: A*AT = I (and det(A) = +/-1).
- A A = AT, making the matrix symmetric rather than orthogonal
- B A*AT = I (and det(A) = +/-1)
- C det(A) = 0, which would make A singular and non-invertible
- D A2 = I, the defining property of an involutory matrix instead
Correct answer: B. A*AT = I (and det(A) = +/-1)
Explanation: Definition: A is orthogonal if its rows (and columns) form orthonormal sets, which means A·Aᵀ = I. Equivalently Aᵀ = A⁻¹. Taking determinants: det(A)·det(Aᵀ) = 1 → det(A)² = 1 → det(A) = ±1. Answer: A·Aᵀ = I (and det(A) = ±1).
Concept context
Evaluation of determinants, cofactors, adjoint, inverse of matrix, Cramer's rule and area applications. Always in board and JEE.