Isomorphism/Inverse mapping/Eigenvalue/Exercise

Let ${}\varphi \colon V\rightarrow V$ be an isomorphism on a ${}K$-vector space ${}V$, and let ${}\varphi ^{-1}$ be its inverse mapping. Show that ${}a\in K$ is an eigenvalue

of ${}\varphi$ if and only if ${}a^{-1}$ is an eigenvalue of ${}\varphi ^{-1}$.

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