Mathematics

Problem

Matrices

A

and

B

satisfy

AB = B^{-1}

, where

B = \begin{bmatrix} 2 & -2 \\ -1 & 0 \end{bmatrix}

, find the value of

\lambda

for which

\lambda A - 2B^{-1} + I = O

, without finding

B^{-1}