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Homework Statement
Let A be an m x n matrix with rank m. Prove that there exists an n x m matrix B such that AB=Im
The Attempt at a Solution
I'm assuming I would need to start with the def. That there exists P an mxm invertible matrix and Q an nxn invertible matrix s.t. A=P(Im 0)Q
then P(Im 0)Q B = Im
now I might multiply left hand side by P inverse and right hand side by Q inverse.
I'm stuck am I going in the right direction?