QUESTION:

Find $\displaystyle A^k$ when:

A = $\displaystyle \begin{bmatrix} -1 & -2 \\ 2 & 3 \end{bmatrix} $

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The eigenvalue (of multiplicity 2) is $\displaystyle x = 1 $

I've tried putting A into Jordan-Normal/Canonical form, but I find that the matrix $\displaystyle (A- x I)^2 = 0 $, and I don't know what to do.

Please help.