Question

Choose the correct answer from the given alternatives in the following question:

If A⁻¹ = `- 1/2[(1,-4),(-1,2)]`, then A = ______.

Options

• `[(2,4),(-1,1)]`

• `[(2,4),(1,-1)]`

• `[(2,-4),(1,1)]`

• `[(2,4),(1,1)]`

Answer 1

`[(2,4),(1,1)]`

Explanation:

A⁻¹ = `1/|"A"|` adj. A

A⁻¹ = `- 1/2[(1,-4),(-1,2)]`

∴ `1/|"A"|` adj. A = `- 1/2[(1,-4),(-1,2)]`

∴ adj. A = `- 1/2[(1,-4),(-1,2)]`

A = `[(2,4),(1,1)]`