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Soit \(A=\left( \begin{array}{cccc} 0&\ldots&0&1\\ \vdots&\mathinner{\mkern 2mu\raisebox{1pt}{.}\mkern 3mu\raisebox{4pt}{.}\mkern 1mu\raisebox{7pt}{.}}&\mathinner{\mkern 2mu\raisebox{1pt}{.}\mkern 3mu\raisebox{4pt}{.}\mkern 1mu\raisebox{7pt}{.}}&0\\ 0& \mathinner{\mkern 2mu\raisebox{1pt}{.}\mkern 3mu\raisebox{4pt}{.}\mkern 1mu\raisebox{7pt}{.}}& \mathinner{\mkern 2mu\raisebox{1pt}{.}\mkern 3mu\raisebox{4pt}{.}\mkern 1mu\raisebox{7pt}{.}}&\vdots\\ 1&0&\ldots&0 \end{array} \right)\)
Montrer que \(A\) est diagonalisable.