If a matrix A is invertible, then it is diagonalizable. Is it true or false?
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3$\begingroup$ True if $A$ is $1\times 1$. $\endgroup$– vadim123Dec 12, 2013 at 18:17
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$\begingroup$ @vadim123 It is somewhat meaningless to talk about diagonalizability in $1\times 1$ though... everything is diagonal in $1\times 1$. $\endgroup$– Sam WongJan 6 at 12:43
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It is false. Consider $\begin{pmatrix} 1 & 1 \\ 0 & 1\end{pmatrix}$
answered Dec 12, 2013 at 17:24
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