Does anyone know how to prove this:

If AB = I, then BA = I also. In other words prove that if B is the right inverse of A, then B is also the left inverse of A.

Thanks.

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- July 7th 2012, 12:25 PMPiIsCoolMatrix Inverse Proof
Does anyone know how to prove this:

If AB = I, then BA = I also. In other words prove that if B is the right inverse of A, then B is also the left inverse of A.

Thanks. - July 7th 2012, 12:44 PMgirdavRe: Matrix Inverse Proof
What are the tools you are allowed to use?

- July 7th 2012, 12:57 PMPiIsCoolRe: Matrix Inverse Proof
I'm pretty much allowed to use anything.

- July 7th 2012, 01:14 PMgirdavRe: Matrix Inverse Proof
If AB=I, then B has full rank. We have B=(BA)B hence (I-BA)B=0. Show that it implies that I-BA=0.