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I know A=[1 1;0 1] and A^{-1}=[1 -1;0 1]

So I know that A and A^{-1}have the same eigenvalues, I know that this is not sufficient to say that A and A^{-1}are similar (or maybe) but the dimension of the Eigenspace with eigen value 1 is 1.

In other words the geometric multiplicity does not equal the algebraic multiplicity.

So does this ultimately mean that A and A^{-1}are not similar?

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# Finding a Matrix that is Similar to A=[1 1;0 1]

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