QUESTION 12 a) Find the order of each element in (Z,+g). 8' b) Find the order of each element in (U (9),.)

Abstract Algebra I

Abstract Algebra I

Matrices and matrix arithmeticLet M2(R) represent the set of all 2 x 2 matrices with entries from the real numbers, let the operation + represent matrix addition, and let the operation * represent matrix multiplication.(Matrix addition and matrix multiplication: if ?= [? ?? ?] and ?= [? ?? ℎ], then ?+?= [?+ ? ?+ ??+ ? ?+ ℎ]; and ?∗?= [??+ ?? ??+ ?ℎ??+ ?? ??+ ?ℎ])a. For the system (M2(R), +), demonstrate or explain why:i. (M2(R), +) is closedii. (M2(R), +) is associative (work out the algebra to prove this)iii. (M2(R), +) has an identity element, i.e., an additive identityiv. Each element in M2(R) has an additive inversev. (M2(R), +) is commutative

Abstract Algebra

[Algebraic Cryptography] How do you solve this?