Other matrix products text reference: section 2., p. 114 set of exercises is to introduce two new the purpose of this the jordan product and the commutator product, and to explore some of their properties. the operations are defined using the ordinary product a b of two n × n matrices. operations on square matrices called the jordan product definition: the jordan product of twon x n matrices a and b is s: 1. why must both a and b be square matrices? 2. calculate the jordan product of the following pairs of matrices. 1 2 and b = 12 1-3 and b32 0 3 5 and b6 7 -5 0 d) a 3. either prove that the following properties are true, or give a counterexample to show that the property does not always hold. all matrices below are assumed to be x , is the n x n identity matrix, and r is any scalar b) (a × b) × c = a × (b × c) c) (a + b) × c = (a × c) + (b × c) the facts shown in items a) and b) above (that the jordan product is commutative but not associative) are used to define algebraic structures called jordan algebras. the peculiar properties of the jordan product make for interesting results in this area of mathematics.