Im having difficulty with the follwing proof ( any help would be appriciated): Let Lambda be and eigenvalue of an invertible matrix A. Show that 1/lambda is and eigenvalue of the inverse of A.
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Necessarily $\displaystyle \lambda\neq 0$ (why?) and there exists $\displaystyle x\neq 0$ such that $\displaystyle Ax=\lambda x$ . Multiply both sides by $\displaystyle A^{-1}$ .
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