JEE Main Mathematics Question (2026) — Solution

Step-by-step solution

The determinant of matrix A is given by: |A| = 1(0 - 3) - 1(-10 - 1) + 2(-6 - 0) |A| = -3 + 11 - 12 = -4 We know the property A( adj A) = |A|I, which gives adj A = |A|A^ -1 . Taking the inverse on both sides: ( adj A)^ -1 = A |A| = A -4 Let B = 2( adj A)^ -1 . Substituting the above expression, we get: B = 2 ( A -4 ) = - 1 2 A We need to find the matrix adj ( adj B). For a square matrix of order n, we have adj ( adj B) = |B|^ n-2 B. Since the order is n = 3: adj ( adj B) = |B|^ 3-2 B = |B|B Now, we calculate the determinant of B: |B| = |- 1 2 A | = (- 1 2 )^3|A| = - 1 8 (-4) = 1 2 Substituting |B| back into the expression for adj ( adj B): adj ( adj B) = 1 2 B = 1 2 (- 1 2 A ) = - 1 4 A The sum of all elements of matrix A is: 1 + 1 + 2 - 2 + 0 + 1 + 1 + 3 + 5 = 12 Therefore, the sum of all elements of the matrix - 1 4 A is: - 1 4 12 = -3 Answer: -3