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> $A\in M\_n(\mathbb{C})$ with all eigenvalues equal to $1$. Suppose the set $\{A^k:k\in\mathbb{N}\}$ be bounded, then show that $A\equiv I$.
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I tried from spectral radius formuale $\displaystyle\lim\_{n\to 0}A^n=0\iff
\rho(A)<1$.

Here $\rho(A)=1$ but then I am lost, please give me hint. Thanks