Let
A = [ 4 0 2 0 3 0 − 1 0 1 ] {\displaystyle A={\begin{bmatrix}4&0&2\\0&3&0\\-1&0&1\end{bmatrix}}}
Write down an invertible matrix P {\displaystyle P} so that P − 1 A P {\displaystyle P^{-1}AP} is a diagonal matrix, or state that no such P {\displaystyle P} exists.
