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## Homework Statement

For p(x)=x

^{4}-2x

^{3}+3x

^{2}-3x+1 and

A= 1 1 1 -1

-1 0 -2 1

0 0 1 0

1 0 0 0

you can check that P(A)=0 using this find a polynomial q(x) so that q(A)=A

^{-1}. The point is A

^{4}-2A

^{3}+3A

^{2}-3A=A(-A

^{3}+2A

^{2}-3A+3I)=I

a) What is q(x)?

I don't really understand how to approach this problem. My initial though was that I had to solve the right side of the eqn(A

^{4}-2A

^{3}+3A

^{2}-3A) and that would be q(x). Am I on the right track? Also what's the purpose of p(x)?

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