Property 1: Associative Property of Multiplication
Given Amxn , Bnxp and Cpxq , then A·(B·C)=(A·B)·C .
Property 2: Multiplication of Matrices is not Commutative
Given Amxn and Bnxm, then A·B ≠
(AB does not have to = BA)
Property 3: Distributive Property of Multiplication
Given Amxn , Bnxp and Cnxp , then A·(B+C)=A·B +A·C
Given Apxq , Bnxp and Cnxp, then (B+C)·A=B·A +C·A
Property 4: Multiplicative identity
Given Amxn, There are unique matrices In and Im with Amxn·In=Amxn and Im·Amxn=Amxn
The matrix In, called the identity matrix or unit matrix of size n is the n-by-n square matrix with ones on the main diagonal and zeros elsewhere.
No se verifica la ley de cancelación
Property 5: Null Matrices may have Non-null Divisors.
The matrix product AB can be zero although A ≠ 0
and B ≠0.
Similar, it is possible that A ≠0, A2 ≠ 0, . . . , but Ap = 0.