# Thread: left inverse equivalent to inverse

1. ## left inverse equivalent to inverse

Hello,

in our lecture the professor said, if a nxn-Matrix M has a left inverse M'*M=I. Then M is invertible.
How can i prove it? I think it is not so easy, since i couldn't solve the problem.

Oh my god. Now i have solved the problem unexpectedly.
Therefore you don't need to answer.

Regards

2. ## Re: left inverse equivalent to inverse

Originally Posted by Sogan
Hello,

in our lecture the professor said, if a nxn-Matrix M has a left inverse M'*M=I. Then M is invertible.
How can i prove it? I think it is not so easy, since i couldn't solve the problem.

Oh my god. Now i have solved the problem unexpectedly.
Therefore you don't need to answer.

Regards
Just out of curiosity, which proof did you use? There are three I can think of.