Matrix Representation of Dual Quaternions

After a review of some properties of dual quaternions, De Moivre`s and Euler`s formulas for the matrices  associated with these quaternions are studied. In special case, De Moivre`s formula implies that there are  uncountably many matrices of unit dual quaternions satisfying  4  n A I = for n≥3. Also; we give the relation  between the powers of matrices of dual quaternions.