Let B be a matrix with characteristic polynomial λ2-λ√6+3. Evaluate B4.
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?