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## Homework Statement

Let B be a matrix with characteristic polynomial λ

^{2}-λ√6+3. Evaluate B

^{4}.

## Homework Equations

B

^{n}=PD

^{n}P

^{-1}

## The Attempt at a Solution

I can find the eigenvalues from the characteristic equation and those would form the diagonal entries of D. But how would I find P, which contains the eigenvectors, if I don't have a matrix?

__Side Note__: How can I quickly find an inverse for a 2 by 2 matrix. Is it just dividing the 2x2 matrix by it's determinant, then negating the diagonal entries going from a11 to a22 and swapping a12 and a21?