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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.