Math Help - 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?

Begin with the following result:

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

Regards.

Fernando Revilla

Using those criteria, I found 6 families. 2 had 1 member, 1 had 2 members, 2 had 3 members, and 1 had 6.

Originally Posted by veronicak5678

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