Let A = bmatrix 1 & 1 & 2 -2 & 0 & 1 1 & 3 & 5 bmatrix . Then the sum of all elements of the matrix adj ( adj (2( adj A)⁻¹)) is equal to:

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|³⁻²B = |B|B Now, we calculate the determ