Find nonsingular matrix C such that C^-1AC is a diagonal matrix

lets say A =

[ 1 0 ]

[ 1 3 ]

I know some properties like the DET will be the same and they have same eigenvalues. I also know if the basis of B (or C^--1AC) is U and the bases for A is E, then U = AE.

However, I don't know how to put all of this together to get the answer. How would I even get the basis of a matrix?