Given M = [[-2,6],[1,3]], find P and D such that M = PDP^(-1) where D is a diagonal matrix

We are given M = [[-2,6],[1,3]], with columns [-2,6] and [1,3]. To find P and D, eigenvalues and eigenvectors must be calculated, as D is defined to be the matrix whose diagonal is comprised of the eigenvalues of M in some order, and P is the matrix of eigenvectors corresponding to the eigenvalues order. We know if e is an eigenvalue and v is an eigenvector, Mv = ev, so Mv - ev = 0 vector, and (M-eI)v = 0 vector, where I is the identity matrix. M-eI has to have determinant 0, so we can solve this equation allowing e to be an unknown variable. by solving for e we obtain e = 4,-3. Returning to the previous equation, (M-eI)v = 0 vector, all that needs to be done is find v for each e. substitute e in the equation, and one can solve for v. To finish, D would be [[4,0],[0,-3]] and P would be [[1,6],[-1,1]]