Let \(A\) be a square real matrix all of whose eigenvalues are zero. Show that \(A\) is diagonalizable (that is, similar to a possibly comples diagonal matrix) if and only if \(A=0\).

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Let \(A\) be a square real matrix all of whose eigenvalues are zero. Show that \(A\) is diagonalizable (that is, similar to a possibly comples diagonal matrix) if and only if \(A=0\).

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