(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let B be a matrix with characteristic polynomial λ^{2}-λ√6+3. Evaluate B^{4}.

2. Relevant equations

B^{n}=PD^{n}P^{-1}

3. 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?

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# Matrix Powers

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