Question

If for a square matrix A, A² – A + I = 0, then A^–1 equals ______.

Options

• A

• A + I

• I – A

• A – I

Answer 1

If for a square matrix A, A² – A + I = 0, then A^–1 equals I – A.

Explanation:

A² – A + I = 0

A^–1A² – A^–1A + A^–1 = 0  ...(Multiplying by A^–1)

A – I + A^–1 = 0

A^–1 = I – A