[1 a {[69] : a € R}. G is a group under the operation of matrix multiplication 01 2. Let G := (you do not need to show that G is a group). Prove that G is isomorphic to R.
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- Let A={ a,b,c }. Prove or disprove that P(A) is a group with respect to the operation of union. (Sec. 1.1,7c)38. Let be the set of all matrices in that have the form with all three numbers , , and nonzero. Prove or disprove that is a group with respect to multiplication.9. Find all homomorphic images of the octic group.
- True or False Label each of the following statements as either true or false. 10. The nonzero elements of form a group with respect to matrix multiplication.True or False Label each of the following statements as either true or false. 9. The nonzero elements of form a group with respect to matrix multiplication.Find the right regular representation of G as defined Exercise 11 for each of the following groups. a. G={ 1,i,1,i } from Example 1. b. The octic group D4={ e,,2,3,,,, }.