Question: 2. For this question let F2 be the set [I], 1} with addition and multiplication mod 2 [the :Elinarj'g.r Field}. Let G = GL[2,]F] the

2. For this question let F2 be the set [I], 1} with addition and multiplication mod 2 [the :Elinarj'g.r Field}. Let G = GL[2,]F] the set of 2 X 2 matrices with elements from F2 with nonzero determinant [in F2} and matrix multiplication. So if .-(;g),.-(g1),.-(13),.-(31),.-(;;),.-(g3), then G = {I,A,B, cans}. {a} Explain why,r GL{2,F2} is the san1e as 3131:1731 F2}. {h} 1Write out the Gayle",r table of G. [a] Is G Abelian? Justify your answer. {d} Find X4 and |X| for every X E G. [e] Find {A}, (B) and {14,3}. [f] Find C(14). {g} Find Zf'}. {h} Find all pmper subgroups of G

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