# Math Help - Matrix Inverse

1. ## Matrix Inverse

How can i show that the matrix inverse exists for A^2 - 3A + I = 0

2. assuming that A is invertible rearrange the equation to make I the subject:
$I = 3A - A^2$
multiply by $A^{-1}$
$A^{-1} = 3I - A$

3. umm.. show that it exists.. not find what it is if it exists

4. Originally Posted by ah-bee
How can i show that the matrix inverse exists for A^2 - 3A + I = 0
$A^2 - 3A + I = 0$

$A^2 - 3A = -I$

$det(A^2 - 3A) = det(-I) \neq 0$

$det(A) . det(A - 3I) = det(-I) \neq 0$

Thus $det(A) \neq 0$