D=(C^(-1))MC
	D is the diagonalized matrix. 
	M is the original matrix.
	 (C^(-1)) is the inverse matrix of C

Clear[M,vecs,A,DD]

M={{a,b},{c,d}}

Determine eigenvalues

Eigenvalues[M]

Create eigenvectors

vecs = Eigenvectors[M]

Transpose eigenvectors to create the C matrix

Transpose[vecs]

Inverse[Transpose[vecs]]

Full application of theorems to diagonalize a square matrix

DD=Simplify[Inverse[Transpose[vecs]].M.Transpose[vecs] ]