Consider the C₃ᵥ point group. The 2×2 matrices shown below form a matrix representation of this group. Use these matrices to evaluate the following combinations of multiple symmetry operations within this group. For example, (E)(σ)v'(σ)v'= (E).
([(E),0],[0,1]), ([-12,-32],[32,-12]), ([-12,32],[-32,-12]) ,([(σ)v,0],[0,-1]), ([-12,32],[32,12]),([-12,-32],[-32,12])
(a) (σ)v(σ)v'(C)₃
(b) (C)₃(σ)v''(C)₃²
