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Can someone provide an example of a $2 \times2$ matrix $A$ where $\operatorname{Col}A = \operatorname{Nul}A$, and explain how this is the case?

In General, under what conditions on $A$, $\operatorname{Col}A = \operatorname{Nul}A$ holds?

Thank you!

Trevor Gunn
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user1519226
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    https://math.stackexchange.com/questions/513347/can-a-matrix-have-a-null-space-that-is-equal-to-its-column-space – JohnColtraneisJC Jul 21 '17 at 03:29
  • $A=\begin{pmatrix}1&0\0&0\end{pmatrix}$. Calculate $\operatorname{Col}A$ and $\operatorname{Nul}A$. For the last question, if $A$ is $n\times n$, then conditions for $\operatorname{Col}A = \operatorname{Nul}A$ is $n=2k$ and $\operatorname{Nul}A=k$. – Aweygan Jul 21 '17 at 04:02

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