Question

Determine if H is subgroup of G, if so prove it, if not explain 1. H...

Determine if H is subgroup of G, if so prove it, if not explain

1. H = {A in GL(2,c): det(A)3 =1}, G = GL(2,c) with matrix multiplication

2. H = {A belongs to GL(n,IR): get(A)=-1}, G=GL(n,IR) with matrix multiplication

3. H = {A belongs to GL(2,IR): AAT=I}, G=GL(2,IR) with matrix multiplication

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Answer #1

In part 3

AA^T=I and since rank(A)=rank(AA^T) implies rank(A)=n

Hence A^-1 exists.

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