Suppose that a $2 \times 2$ matrix $A$ has an eigenvalue $3$ with corresponding eigenvector $\left[\begin{array}{c} -1\cr 2 \end{array}\right]$ and an eigenvalue $-1$ with corresponding eigenvector $\left[\begin{array}{c} 1\cr -1 \end{array}\right]$.

Find an invertible matrix $P$ and a diagonal matrix $D$ so that $A = P D P^{-1}$. Enter your answer as an equation of the form $A = P D P^{-1}$. You must enter a number in every answer blank for the answer evaluator to work properly.

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