Discussion
A matrix satisfies the relation that its square equals itself. Its eigenvalues can only be
Answer: C
Applying \( A^{2}=A \) to an eigenvector \( x \) with \( Ax=\lambda x \):
\[ A^{2}x = \lambda^{2}x \quad\text{and}\quad Ax = \lambda x \quad\Rightarrow\quad \lambda^{2} = \lambda \]
\[ \lambda(\lambda-1)=0 \quad\Rightarrow\quad \lambda = 0 \text{ or } 1 \]
An involutory matrix, satisfying \( A^{2}=I \), instead admits only \( \lambda = \pm 1 \).
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