Column space of $A^*$ is row space of $A$?

33 Views Asked by At

I have seen that range $A^*$ = $(\text{null }A)^\perp$, for example here. And I have seen that $(\text{null A})^\perp$ = row $A$, for example here. Does it therefore follow that range $A^*$ = row $A$? I haven't seen this written anywhere, and it seems like such a simple relationship that, if it were true, it would pop up on the internet somewhere. So what am I missing? Or is it just true?