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

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- May 12th 2008, 10:54 PMah-beeMatrix Inverse
How can i show that the matrix inverse exists for A^2 - 3A + I = 0

- May 12th 2008, 11:41 PMDr Zoidburg
assuming that A is invertible rearrange the equation to make

*I*the subject:

$\displaystyle I = 3A - A^2$

multiply by $\displaystyle A^{-1}$

$\displaystyle A^{-1} = 3I - A$ - May 12th 2008, 11:54 PMah-bee
umm.. show that it exists.. not find what it is if it exists

- May 13th 2008, 01:44 AMIsomorphism