Let A = a i j be a 3 × 3 matrix, where a i j = - 1 j - i       if   i < j 2                 if   i = j - 1 i + j       if   i > j then det 3 Adj 2 A - 1 is equal to ________.

Step-by-step solution

We have, a i j = - 1 j - i       if   i < j 2                 if   i = j - 1 i + j       if   i > j The, A = 2 - 1 1 - 1 2 - 1 1 - 1 2 ⇒ A = 4 Now, 3 adj 2   A - 1 = 3 3 adj 2 A - 1 ∵ k adj A - 1 = k n adj A - 1 ⇒ 3 adj 2   A - 1 = 3 3 · 2 6 A - 1 2 ∵ adj k A - 1 = k n - 1 n adj A - 1 = k n - 1 n A - 1 n - 1 ⇒ 3 adj 2   A - 1 = 12 3   A - 1