JEE Main 2025 Mathematics question
Let a ∈ R and A be a matrix of order 3 × 3 such that det(A) = –4 and A + I = , where I is the identity matrix of order 3 × 3. If det ((a + 1) adj((a – 1)A)) is , m, n ∈ {0, 1, 2, …, 20}, then m + n is equal to :
Answer: (1)
Solution
A = [[0,a,1],[2,0,0],[a,1,1]]; |A| = –4 gives –2a+2 = –4, a=3. Then |4adj(2A)| = 4³|2A|² = 4³·2⁶·|A|² = 2¹⁶·3⁰, so m+n = 16.