What are the only two possible eigenvalues for an idempotent matrix (where A² = A)?
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0 and 1
Idempotent matrices represent projections. Since applying a projection twice is the same as applying it once, the eigenvalues must satisfy the equation x² = x, which only allows for 0 and 1.
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- If a matrix satisfies $A^2 = A$, what are its only possible eigenvalues?