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If a matrix A is invertible, then it is diagonalizable. Is it true or false?

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    $\begingroup$ True if $A$ is $1\times 1$. $\endgroup$ Commented Dec 12, 2013 at 18:17
  • $\begingroup$ @vadim123 It is somewhat meaningless to talk about diagonalizability in $1\times 1$ though... everything is diagonal in $1\times 1$. $\endgroup$ Commented Jan 6, 2023 at 12:43

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It is false. Consider $\begin{pmatrix} 1 & 1 \\ 0 & 1\end{pmatrix}$

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    $\begingroup$ I love minimal counterexamples. $\endgroup$ Commented Dec 12, 2013 at 17:27

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