Answer to Question #214749 in Real Analysis for hussein

Question

r the set of all 2*2 commutative and invertible matrices with real entries Does R from a filed ? prove your assertion . Determine whether R2*2 (R) from order filed or not ? if your answer is no can we define an order such that R 2*2 (R) from an order filed ? prove tour assertion

Answer 1

The set of all 2 by 2 Matrices with the usual operations of matrices addition and multiplication is a ring. So if we add commutativity and inverse operations we have a field in our hands.

This field is not ordered, because there is no way we can compare matrices in such a sense.

And we so cannot define such an order.