If A^2 - A + 1 = 0, then the inverse of A is :

Question

If ${A^2} - A + 1 = 0$, then the inverse of $A$ is :

Accepted Answer

Given ${A^2} - A + I = 0$

$${A^{ - 1}}{A^2} - {A^{ - 1}}A + {A^{ - 1}}.I = {A^{ - 1}}.0$$

(Multiplying $$\,\,\,{A^{ - 1}}$$ on both sides)

$$ \Rightarrow A - 1 + {A^{ - 1}} = 0$$

or ${A^{ - 1}} = 1 - A$

Solutions · 1