# Math Help - Eigenvalue

1. ## Eigenvalue

How do I go about solving this problem?

2. 1 is an eigenvalue of A means $det(A-I)=0$
So if we could try to get some value x such that $A^{2010}-2A+3I-xI$ can factor out an A-I, then we're done (using $det(MN)=det(M)det(N)$). Clearly x=2 works.