
Find nosingular matrix
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?

What's normally done, assuming you can do this (not always true), is that you construct the diagonal matrix out of the eigenvalues of A, and you construct the columns of C out of the eigenvectors of A. So, solve the eigenvalue problem for A, and post what you get.

Thanks, I managed to work it out

You're welcome. Have a good one!