Can you help me prove this statements.

Let A be a ring, and A, B be 2 matrixs. if

and then m=n.

Im and In are identity marix.

Thank you .

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- June 18th 2013, 08:13 AMjohn27Let A be a ring, prove that if AB=I and BA=I .....
Can you help me prove this statements.

Let A be a ring, and A, B be 2 matrixs. if

and then m=n.

Im and In are identity marix.

Thank you . - June 18th 2013, 11:30 AMDrexel28Re: Let A be a ring, prove that if AB=I and BA=I .....
Think about it like this. You have shown that is an isomorphism of . Assuming that is commutative (so that it has the invariant basis number property) then .

Best,

Alex - June 19th 2013, 05:50 AMjohn27Re: Let A be a ring, prove that if AB=I and BA=I .....
Yes A is a commutative Ring with identity . Is n=m ?

- June 19th 2013, 07:10 AMHallsofIvyRe: Let A be a ring, prove that if AB=I and BA=I .....
Yes, that is what Drexel28 said. By the way, you should

**never**use the same symbol to mean two different things- here you use "A" to mean both the ring and an element of the ring.