ABSTRACT
Multiply the 3 x 2 matrix C by the scalar a = 2 to obtain the 3 x 2 matrix D. From Eq. (1.23), d ll = aC11 = (2)(10) = 20, d l2 = aCI2 = (2)(8) = 16, etc. The result is
D = aC = 2C = (2)(13) (2)(8) = 26 16 (2)(12) (2)( 12) 24 24
Matrices that are suitably conformable are associative on multiplication. Thus,
A(BC) = (AB)C ( 1.29) Square matrices are conformable in either order. Thus, if A and Bare n x n matrices,
AB=C and BA=D ( 1.30) where C and Dare n x n matrices. However square matrices In general are not commutative on multiplication. That is, in general,
AB oj:: BA (1.31) Matrices A, B, and C are distributive if Band C are the same size and A is conformable to Band C. Thus,
A(B + C) = AB + AC Consider the two square matrices A and B. Multiplying yields
( 1.32)
(1.33) It might appear logical that the inverse operation of multiplication, that is, division, would give
A=C/B (1.34) Unfortunately, matrix division is not defined. However, for square matrices, an analogous concept is provided by the matrix inverse.
