If $n\times n$ matrix A is symmetric, is $A^{10}$ symmetric also? All I can deduce is that $A^{T}=A$, but that doesn't give me much in trying to show that $A^{10}$ is symmetric. Any hints/suggestions?
2026-03-28 21:51:44.1774734704
If $n\times n$ matrix A is symmetric, is $A^{10}$ symmetric also?
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Hint. $(AB)^T = B^T A^T$. Now use induction.