- #1

JKCB

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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?