The question that I am trying to solve is
Suppose that A is n × n and has rank n. What is its row space? What is its nullspace? What is its column space?
From rank nullity theorem, I know that the null space will be 0 because. Also, rank = dim(column space(A)) = dim(row space(A))
But the question asks for the row space and column space and not the dimensions of those. How can I find those two without knowing what the actual matrix is? Any help will be really appreciated. Thank you!
If $T: V\to V$, and the rank equals $n$, the dimension of $V$, then the range, column space, and row space are necessarily $V$.