How does matrix algebra differ from the *usual* algebra of numbers. Give several examples to demonstrate some of the differences.

1. How does matrix algebra differ from the *usual* algebra of numbers. Give several examples to demonstrate some of the differences. For example, you might find two matrices and which do not have the commutative property for multiplication.2. What similarities and differences are there between matrix algebra and other algebras we have seen in this course, namely the algebra of sets and the algebra of logic. Again, there are some similarities and some differences. Give concrete examples. You may find it useful to read scetion 5.6 and consider the supplemental exercises from section 5.6.