The sum of the elements of U^-1 is (A) -1 (B) 0 (C) 1

Question

Let A = [(1, 0, 0), (2, 1, 0), (3, 2, 1)]. If U₁, U₂ and U₃ are columns matrices satisfying

AU₁ = [1, 0, 0], AU₂ = [2, 3, 0], AU₃ = [2, 3, 1] and U is 3 × 3 matrix whose columns are U₁, U₂ and U₃ then

The sum of the elements of U^-1 is

(A) -1

(B) 0

(C) 1

(D) 3

Answer 1

Answer is (B) 0

Hence, U^-1 = adjU/3 and the sum of the elements of U^-1 = 0