SOLUTION: If A and B are (nxn) matrices such that A is non singular and AB = 0 , then prove that B = 0 .

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Question 429449: If A and B are (nxn) matrices such that A is non singular and AB = 0 , then prove that B = 0 .
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
AB+=+O ==> A%5E%28-1%29%2A%28AB%29+=+A%5E%28-1%29%2AO since A is nonsingular.
==> B+=+O, the zero matrix, since A%5E%28-1%29%2AO+=+O, and A%5E%28-1%29A+=+I%5Bn%5D