 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/12/b/iii/solution

A^{2} = - I /4

. Therefore

A (- 4 A) = I = (- 4 A) A

, yielding

A^{2} = (- 1/4 0 0 - 1/4), A^{- 1} = - 4 A = (02 - 2 0) .

The nonzero determinant ensures that this two-sided inverse is unique as a matrix inverse.

 New to topics? Read the docs here!