Linear Algebra question matrix multiplication

label Mathematics
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Which of the following may not be true for matrix multiplication even when the operations are defined?

a) Commutative

b) Associative

c) Multiplication is distributive over addition

Mar 1st, 2015

Please your answer is option a)

The algebra of matrices is not commutative, namely different operators don't commute each other, it is a fundamental characteristic of Quantum Mechanics.

In Quantum Mechanics the non-commutativity of the algebra of the operators, is expressed by the introduction of the commutator operator. Namely if I have two operators, represented by the matrices A, B, then the commutator operator is defined as follows:

[A,B] = A*B - B*A, which, of course is not equal to zero, in general. For example the commuattor between the operators coordinate and momentum is:

[x, p] = i* h/(2*pi), where i is such that i^2=-1 and h is the Planck constant, and pi = 3.14159...

Mar 1st, 2015

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