Question

If A^–1  = `[(3, -1, 1),(-15, 6, -5),(5, -2, 2)]`, then adj A = ______.

Options

• I

• A

• A^–1 

• 2A^–1 

Answer 1

If A^–1  = `[(3, -1, 1),(-15, 6, -5),(5, -2, 2)]`, then adj A = A^–1 .

Explanation:

AA^–1 = I

∴ `"A"[(3, -1, 1),(-15, 6, -5),(5, -2, 2)] = [(1, 0, 0),(0, 1, 0),(0, 0, 1)]`

∴ `"A"[(1, 0, 0),(0, 1, 0),(0, 0, 1)] = [(2, 0, -1),(5, 1, 0),(0, 1, 3)]`

∴ A = `[(2, 0, -1),(5, 1, 0),(0, 1, 3)]`

|A| = 1

A^–1 =`1/|"A"|` adj A

∴ A^–1 = adj A