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Math Help - Show 1/lambda = eigenvalue of A^-1

  1. #1
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    Show 1/lambda = eigenvalue of A^-1

    I am not sure where to begin with this question but any guidance will be greatly appreciated:

    Question: Let A be a nonsingular matrix and let lambda be an eigenvalue of A. Show that 1/lambda is an eigenvalue of A^-1
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    If A\in \mathbb{K}^{n\times n} is nonsingular and \lambda \in \mathbb{K} is an eigenvalue of A then, \lambda\neq 0 (why?) and there exists 0\neq x \in \mathbb{K}^n column vector such that Ax=\lambda x . Now, multiply both sides by A^{-1} .


    Fernando Revilla
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