Question: Hi can we have help with this please 3. Consider the following subset H of GL2(R) H= ((c d) : a,b. c, d EZ, ad

Hi can we have help with this please

3. Consider the following subset H of GL2(R) H= ((c d) : a,b. c, d EZ, ad - bc = +1 (a) Show that H is a subgroup of GL2(R) [3] (b) Let P = and 0 be the map that sends M to PMP-1 for all ME H. Prove that 0 is a map from H to H. [2] (c) Prove 0 is an isomorphism. [3] (d) Hence, or otherwise, show that for all (a b) EH. (2 8) has man and only if (b+d. a+c-b-d) b , . a - b has infinite order. [21

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