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Question: please help me with number 9...

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please help me with number 9(b) Prove: If A, B E GL(n, R), then AB E GL(n, R) and A-1 E GL(n, R). Conclude that GL(n, R) is a group under the operation of matrix multiplication. (c) Let SL(n,R) be the set of all n x n matrices A with det(A) = 1, Prove: SL(n, R) is a normal subgroup of GL(n, R). [You must prove that it is a subgroup, and also that it is normal.] (d) Let Ф : GL(R)-+ GL(n,R) be the function which associates to each invert- ible linear operator T the matrix representing T with respect to the standard basis for R. Prove: Ф is an isomorphism of groups 9(a) Prove: The relation of similarity is an equivalence relation on the set of all (b) Prove: A subgroup H of a group G is normal if and only if H is a union of 10. Let II be a plane passing through (0,0,0) in R3 with equation: n × n matrices. conjugacy classes of G. ar + by+ cz-0 Let Rm: R3 R3 be the reflection map across the plane 1. Let Pa : R3-R3 be the orthogonal projection map onto the line through the normal vector n- (a, b, c) to the plane 11, Let ph : R3 → R3 be the orthogonal projection map onto the plane п.

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