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## Homework Statement

Proof: Prove that if A is an nxn (square mtx) such that A^2=A, then A has 0 or 1 as an eigenvalue.

## The Attempt at a Solution

A=A^2

A^2-A=0

A(A-I)=0

A=0 or A=1

and then plugging the A solutions in to the characteristic equation and solving for λ