Answer:
PROOF:
Suppose that A is an invertible non singular matrix.
Then,
[tex]Ax=\lambda x\\\\A^{-1}Ax=A^{-1}\lambda x\\\\\frac{1}{\lambda}x=A^{-1}x\\\\\lambda^{-1}x=A^{-1}x[/tex]
This shows that if A is non singular invertible matrix ad if λ is eigenvalue of A then λ⁻¹ is eigenvalue of A⁻¹.
