Question

If A = `[(1, 2, -1),(-1, 1, 2),(2, -1, 1)]`, then det (adj (adj A)) is ______.

Options

• (14)⁴

• (14)³

• (14)²

• (14)¹

Answer 1

If A = `[(1, 2, -1),(-1, 1, 2),(2, -1, 1)]`, then det (adj (adj A)) is (14)⁴. 

Explanation:

We know that

adj (adj A) = |A|^n–2 A, if |A| ≠ 0, provided order of A is n.

∴ adj (adj A) = |A| A (as n = 3)

∴ det (adj (adj A)) = |A|³ det A = |A|⁴ 

But |A| = `[(1, 2, -1),(-1, 1, 2),(2, -1, 1)]` = 14

∴ det (adj (adj A)) = (14)⁴