 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2003/paper-1/5/b/ii/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

Again take

A = B = I_{2}

. Their sum is also invertible, but

(A + B)^{- 1} = I_{2} /2

, while

A^{- 1} + B^{- 1} = 2 I_{2}

. Thus matrix inversion is not additive, even when every inverse in the proposed identity exists.

 New to topics? Read the docs here!