JEE Main 2024 Mathematics question
Let A be a 3 × 3 matrix of non-negative real elements such that . Then the maximum value of det(A) is .
Answer: 27
Solution
Each row sums to 3 with non-negative entries; by Hadamard's inequality det A ≤ ∏‖row‖, and the maximum 27 is attained by A = 3I.