Diagonalize $\begin{bmatrix} 5 & 0 & 0\\ 1 & 5 & 0\\ 0 & 1 & 5\\ \end{bmatrix}$ and find P and D such that $P^{-1}AP=D$
So I created the matrix $\begin{bmatrix} \lambda-5 & 0 & 0\\ -1 & \lambda-5 & 0\\ 0 & -1 & \lambda-5\\ \end{bmatrix}$
Finding the determinant gives me $(\lambda-5)^3$ so $\lambda=5$
Subbing this in gives $\begin{bmatrix} 0 & 0 & 0\\ -1 & 0 & 0\\ 0 & -1 & 0\\ \end{bmatrix}$ and I am unsure where to go from here?