# Math Help - Eigenvalue algebra proof question

1. ## Eigenvalue algebra proof question

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.

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