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bcjochim07
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Homework Statement
If A is an idempotent matrix (A^2 = A), find all possible values of det(A).
Homework Equations
The Attempt at a Solution
I'm not sure if this is the proper way to show it, but here's what I did:
Since A = A^2, det(A)=det(A^2)
So det(A) = det(A)*det(A)
Considering two cases:
If det(A) is not 0, then
det(A) = 1.
The only other way to satisfy det(A) = det(A)*det(A)
is if det(A) = 0.
So det(A) is either 1 or 0.