Let A be a 3 × 3 matrix such that adj A = [(2, -1, 1) (-1, 0, 2) (1, - 2, -1)] and B = adj (adj A). If |A| = λ and |(B^–1)^T| = μ ,

Question

Let A be a 3 × 3 matrix such that adj A = \(\begin{bmatrix} 2&-1&1\\-1&0&2\\1&-2&-1 \end{bmatrix}\)and B = adj (adj A).

If |A| =  λ and |(B^–1)^T| = μ , then the ordered pair, (|λ|, μ) is equal to :

(1) \((9,\,\frac{1}{9})\)

(2) \((9,\,\frac{1}{81})\)

(3) \((3,\,\frac{1}{81})\)

(4) \((3,\,{81})\)

Answer 1

 (3) \((3,\,\frac{1}{81})\)