# Matrixes Arithmetic

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• January 16th 2010, 11:11 AM
Bungkai
Matrixes Arithmetic
Show that if a square matrix A satisfies $A^2 - 3A + I = 0$ then $A^-1 = 3I - A$

I tried to solve from a series of equations, but it just went in circles.
• January 16th 2010, 11:28 AM
Dinkydoe
Given is: $A^2-3A+I = 0 \Longrightarrow I = -A^2+ 3A$

Now observe that $A(3I-A) = -A^2+3A = I$. Hence $A^{-1} = 3I-A$