Eigenvalue algebra proof question

**kensington** · February 24th 2011, 02:03 PM

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.

**FernandoRevilla** · February 24th 2011, 02:19 PM

Necessarily $\lambda\neq 0$ (why?) and there exists $x\neq 0$ such that $Ax=\lambda x$ . Multiply both sides by $A^{-1}$ .

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