How could we prove that
If $\lambda_1,\lambda_2,\lambda_3,\cdots \lambda_n $ are the eigenvalues of a non-singular square matrix $A$ then eigenvalues of adj $\space A$ are $\frac {\det A}{\lambda_1},\frac {\det A}{\lambda_2},\frac {\det A}{\lambda_3},\cdots \frac {\det A}{\lambda_n}$.
I stumbled upon this property while solving a MCQ type question, in the solution there is no proof, I was just wondering if anybody could show me how to prove this one.
Thanks,