If columns/rows of an $n\times n$ matrix $M$ are linearly independent what is the rank of $M$?

Question

1.) I think I can answer the case when the rows are linearly independent vectors:

Since the rows of the matrix $M$ are linearly independent, we cannot create an all $0$ row in the matrix therefore the $rank(M) = n$.

2.) How do you proceed if you want to deduce a similar result for the case when the columns are linearly independent?

Answer 1

TIP: $col(A)=row(A^T)$ and $rank(A^T)=rank(A)$

You should study the Fundamental Theorem for invertible matrices for proofs.