Let A be a square matrix such that AAᵀ = I. Then 12A [(A + A^T)^2 + (A - A^T)^2 ] is equal to-

JEE Main 2024 Mathematics question

Let A be a square matrix such that AAᵀ = I. Then is equal to-

Answer: (D)

(A + Aᵀ)² + (A − Aᵀ)² = 2A² + 2(Aᵀ)² (the cross terms cancel). So the expression is A(A² + (Aᵀ)²) = A³ + AAᵀAᵀ = A³ + Aᵀ, using AAᵀ = I.

Question ID VK-016911