Show that the relation on the set of all 2 x 2 matrices defined by A~B if detA = detB is an equivalence relation. Describe the equivalence class.
I've never shown an equivalence relation on a set of matrices before. I've determined that the set is reflexive as two matrices with the same values will have the same determinant. I'm fairly certain that the set is also transitive and symmetric, however, I am not clear on how to prove it.
I've never shown an equivalence relation on a set of matrices before. I've determined that the set is reflexive as two matrices with the same values will have the same determinant. I'm fairly certain that the set is also transitive and symmetric, however, I am not clear on how to prove it.
