Let A = bmatrix 4 & -2 & bmatrix . If A^ 2 + A + 18I = 0, then det(A) is equal to _____ .

JEE Main 2022 Mathematics question

Let A = . If , then det(A) is equal to .

Answer: (2)

By the Cayley–Hamilton theorem, A satisfies its characteristic equation , i.e. $ -

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Question ID VK-034329