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## Homework Statement

A square matrix P is called an idempotent if P^2 = P,

Show that if A is n x m and B is m x n, and if AB = In, then BA is an idempotent

## Homework Equations

## The Attempt at a Solution

I have this one identity I think, but I'm not sure how to use it?

If A is m x n, then ImA = A = AIn

B*In*In*A

can I do anything with that?

My inverse definition shows for square matrices... how does it apply for non-square matrices? Or how can I use it?