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?
Begin with the following result:
Two similar matrices have the same trace and the same determinant.
Regards.
Fernando Revilla
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