### Groups and Representations

Please help answer the following algebra questions. Provide step-by-step solutions. (i) Now let G be a group with the presentation G=<a,b|a^7=e,b^3=e,b^(-1) ab=a^2> You are told that |G|=21. Let w=exp(2i*pi/(7)) E C. Prove that there is a representation p:G --> GL(3,C) with p(a)= (w^2, 0, 0; 0, w^4, 0; 0, 0, w) and p(