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  1. #1
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    center

    how do you find the center of a 2x2 matrix group where elements all have det + 1 or -1.

    isit -I and I?

    what about the center when the determinant of the elements in the group all have det=1?
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    how do you find the center of a 2x2 matrix group where elements all have det + 1 or -1.

    isit -I and I?
    Assume your matrix group is over the field K. Then, the center consists of all scalar matrices whose determinant is 1 or -1.

    what about the center when the determinant of the elements in the group all have det=1?
    Similarly, the center consists of all scalar matrices whose determinant is 1.

    In this case, the center is isomorphic to the group of n-th roots of unity in K.

    Edit: In this case, just n=2.
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    For both groups, the center is Z=\{I,-I\} .


    Edited: Sorry, I didnīt see TheArtofSimmetry's post.
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