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Let $L$ be an $n \times n$ matrix with real entries and let $\lambda$ be an eigenvalue of $L$. In the following list, identify all the assertions that are correct.
a) $a \lambda$ is an eigenvalue of $a L$ for any scalar $a$.
b) $\lambda^{2}$ is an eigenvalue of $L^{2}$.
c) $\lambda^{2}+a \lambda+b$ is an eigenvalue of $L^{2}+a L+b I_{n}$ for all real scalars $a$ and $b$.
d) If $\lambda=a+i b$, with $a, b \neq 0$ some real numbers, is an eigenvalue of $L$, then $\bar{\lambda}=a-i b$ is also an eigenvalue of $L$.
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