Consider the matrix 1 1 1 ба = √3 31+i - -1 (i) Find the powers of this matrix (σa) for any integer m. ... [5] (ii) Either by using (i) and the Taylor expansion for the exponen- tial function, or the matrix constructed from the eigenfunction of σa, evaluate the expression U = eipoa where is a real number, and show that det|U| = 1, i.e. it is a rotation matrix. {Hint: The Taylor series method may work faster. } (iii) Show that ... [5] ... [10] icot (1U). (1+U)¯¹ = σa· 12.(1