1. ## Identity Matrices

i have this question and im havint trouble solving it, anyone have any idea?

A matrix A obeys the matrix equation A3=2A + I where I is the identity matrix of appropriate order. The inverse A1 Is given by :

any help would be much appreciated!

2. Originally Posted by sebko
i have this question and im havint trouble solving it, anyone have any idea?

A matrix A obeys the matrix equation A3=2A + I where I is the identity matrix of appropriate order. The inverse A1 Is given by :

any help would be much appreciated!
Left multiply both sides of the expression by the inverse matrix:

$\displaystyle A^3 = 2A + I \Rightarrow A^2 = 2I + A^{-1}$.