I came across this question but I'm not sure how to approach it; My thought process is that by definition all subgroups are groups, then why would it be a different case for matrices? What are some cases that I have to consider?
2026-03-25 17:45:32.1774460732
Are normal subgroups of a matrix group a matrix group?
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A matrix group is just a set of matrices with the group structure being matrix multiplication! A subgroup of a group is just a subset with the same group structure (in particular this subset is closed under the group action and inverses exist). So any subgroup of a matrix group is a matrix group (you don’t need normality). You just restrict the set of matrices you’re working with!