How to find eigenvalues and eigenvector in python without Numpy library?
If you really want to avoid using numpy.linalg (why? This must be some sort of a learning problem, surely), you can e.g.  implement a variant of a qr algorithm: factorize A into the product of Q@R, multiply R@Q, repeat until convergence.
However, if it's indeed a learning exercise, your best bet is to pick a textbook on numerical linear algebra.
And if it is not, then keep in mind that you are very unlikely to outperform (in any definition of performance) the tried-and-tested lapack routines that numpy.linalg wraps.
I am trying to find eigenvalues and eigenvector in python without Numpy but I don't know how to calculate det(A-lemda*I) for finding eigenvalue.