JEE Main 2022 Mathematics question

Let A be a matrix with det(A) = −1 and det((A + I)(Adj(A) + I)) = 4. Then the sum of the diagonal elements of A can be

Answer: (2)

Solution

(A + I)(adj A + I) = A adj A + A + adj A + I = |A|I + A + adj A + I = A + adj A (since |A| = −1). For A = , adj A =

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Question ID VK-025167