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Math Help - Similar Matrices

  1. #1
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    Similar Matrices

    There are 16 2x2 matrices with only entries of 0 or 1. If similar matrices form a family, how many families of these matrices are there? How many matrices in each family?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Begin with the following result:

    Two similar matrices have the same trace and the same determinant.

    Regards.

    Fernando Revilla
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    Using those criteria, I found 6 families. 2 had 1 member, 1 had 2 members, 2 had 3 members, and 1 had 6.
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by veronicak5678 View Post
    Using those criteria, I found 6 families. 2 had 1 member, 1 had 2 members, 2 had 3 members, and 1 had 6.
    That is not correct. There are 8 families: 4 have 1 element, 3 have 2 elements and 1 has 6 elements.

    Take into account that the conditions about trace and determinant are necessary, not sufficient.

    Regards.

    Fernando Revilla
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