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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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 .
Yes A is a commutative Ring with identity . Is n=m ?
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.
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