5. Let (G;*] be a group, and let a, b, c E G. (a) Solve the equation b***a? = a*c*a for r EG. Simplify your answer. (b)

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5 Let G Be A Group And Let A B C E G A Solve The Equation B A A C A For R Eg Simplify Your Answer B 1 (40.2 KiB) Viewed 23 times

5. Let (G;*] be a group, and let a, b, c E G. (a) Solve the equation b***a? = a*c*a for r EG. Simplify your answer. (b) Expand and simplify the following expression: (b***b-1)3 6. In each part, a group (G; *) and two elements X, Y of G are given. Compute X4, X-3, and (X+Y)-4. Also, state the identity for each group. (Note: Each group has a standard binary operation - use this for * in each part.) (a) Group: Z6 XZ Elements: X = (3,5), Y = (2,7) (b) Group: R* RXR Elements X = (3, 1,4), Y = (7,2,5).