Question

If A and B are invertible matrices, then which of the following is not correct?

Options

• (A + B)⁻¹ = B⁻¹ + A⁻¹

• (AB)⁻¹ = B⁻¹ A⁻¹

• adj (A) = |A| A⁻¹

• |A|⁻¹ = |A⁻¹|

Answer 1

(A + B)⁻¹ = B⁻¹ + A⁻¹

Explanation:

(AB)⁻¹ = B⁻¹ A⁻¹

|A|⁻¹ = |A⁻¹|

adj A = |A| A⁻¹

(A + B)⁻¹ ≠ B⁻¹ + A⁻¹