I'm not really sure where to go with this question, any help would be appreciated.

Question

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.

Attempt

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.

  • @hjpotter92 Thanks for editing the body of the post. It's best to also edit the title along with the body, when needed (as it was here). – user147263 Nov 2 '15 at 12:52

If $A$ is row-equivalent to say $B$ and $B$ is invertible, then thre exist elementary matrices $E_1,\dots,E_r$ such that $B=E_r\dots E_1A$. Now, each $E_i$ is invertible. So, is a product of invertible matrices.

Your Answer

 

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.