Is the set 1,2,3,4,5,7} a group under addition modulo 7.(b) Is the above set a group under multiplioation modulo 7.

Let G = 1,2,3,4,5,6}. Find the order of all the elements of G under the binary operation“multiplioation modulo 7”

Prove that follo ing set forms a group under multiplioation.[1 00 0] , [-1 00 1] , [1 00 -1] , [-1 00 -1]}

Match a with b so that a is congruent to b modulo 7.a = 23Answer 1a = 11Answer 2a = 17Answer 3

Given that ϕ is a isomorphism from a group G under addition to a group G under addition, convert property 2 of Theorem 6.2 to additive notation.

Let 𝐺 = [𝑎 00 0] : 𝑎 𝑖𝑠 𝑎 𝑛𝑜𝑛 − 𝑧𝑒𝑟𝑜 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 } . hho that 𝐺 is a oommutativegroup under multiplioation