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

Re: left inverse equivalent to inverse

Quote:

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.