# Matrix Inverse

• May 12th 2008, 11:54 PM
ah-bee
Matrix Inverse
How can i show that the matrix inverse exists for A^2 - 3A + I = 0
• May 13th 2008, 12:41 AM
Dr Zoidburg
assuming that A is invertible rearrange the equation to make I the subject:
$I = 3A - A^2$
multiply by $A^{-1}$
$A^{-1} = 3I - A$
• May 13th 2008, 12:54 AM
ah-bee
umm.. show that it exists.. not find what it is if it exists
• May 13th 2008, 02:44 AM
Isomorphism
Quote:

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 $det(A) \neq 0$