I'm not really sure where to go with this question, any help would be appreciated.
Let $A$ be an $n\times n$ matrix. Prove that if $A$ is row equivalent to some invertible $n\times n$ matrix $B$ then A is invertible.
I'm not sure where a starting point would be. I know that an $n\times n$ matrix B is invertible if there is a matrix A such that B is both the left and the right inverse of A: AB = In and BA = In, but I'm not sure if this would be useful.