# Modern algebra

(a) Let G = GL(2,R) be the general linear group. Let

H=GL(2,Q) and K= SL(2,R) = {A is an element of G: det (A) =1} Show that H,K are subgroups of G

(b) Let p be a prime number and a is an element of Z. Prove that a^p ,is equivalent to, a mod p

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