Eigen-values of a matrix $P^{-1}AP$ 
QUESTION: If A and P be $2$ non-singular $n\times n$ matrices and $\lambda$ is the eigen-value of $A$, then show that $\lambda$ is also
  the eigen-values of a matrix  $P^{-1}AP$.

I could simply show that $\lambda$ being the eigen-value of $A$, we have that 
$$det (A-\lambda I_n)=0$$
But I could not proceed further and make any comment on the question asked. 
NOTE: I am unaware of diagonalisation of matrices, if at all it is playing any part in this problem. And also I require a method which does not utilise this principle of diagonalisation to solve this.

It's just that $$P^{-1}AP-\lambda I=P^{-1}(A-\lambda I)P. $$
