- #1

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- Homework Statement
- If AB = I for square matrices A and B, show that B is invertible. (Do not assume A is invertible)

- Relevant Equations
- ##A.A^{-1}=I##

Definition of inverse: Matrix ##P## is invertible if there is matrix ##Q## such that ##PQ = I## and ##QP = I##

So since ##AB = I## is given, first I need to show ##BA = I## to be able to prove that ##B## is invertible? If yes, how to show ##BA = I##?

I thought the answer to this question is straightforward, because ##AB = I##, it means that ##A## is inverse of ##B##, so ##B## has inverse then ##B## is invertible?

Thanks

So since ##AB = I## is given, first I need to show ##BA = I## to be able to prove that ##B## is invertible? If yes, how to show ##BA = I##?

I thought the answer to this question is straightforward, because ##AB = I##, it means that ##A## is inverse of ##B##, so ##B## has inverse then ##B## is invertible?

Thanks