# VUB Chair lecture- The order of the factors DOES CHANGE the product

School children are taught the commutativity property in the negative form of what is written in the title. For example 4x5=5x4=20.

This is valid for the standard multiplication of numbers but fails for many other kinds of product, such s as for example the product of matrices or the rotation of solids.

Actually, everybody knows that it is not the same to first put on a sock and then a shoe rather than than the other way around.

During this lecture Prof. Dr. Ángel del Río will show examples of non-commutative objects and explain some of the questions on this topic that mathematicians have not been able to solve yet.

The lecture is followed by a reception.

Website of Prof. Dr. Ángel del Río Mateos

Professor Dr. Ángel del Río is full Professor at the University of Murcia, Spain. He's an expert in Group and Ring Theory and a top specialist in the unit group of group rings and orders. He has more than 75 publications in international magazines and he published 4 books.