Adding Matrices
Given two matrices of the same dimension, A = (aij) and B = (bij), the matrix sum is defined as: A + B = (aij + bij). That is, the resultant matrix's elements are obtained by adding the elements of the two matrices that occupy the same position.
Properties of the Addition of Matrices
Closure:
The sum of two matrices of dimension m x n is another matix of dimension m x n.
Associative:
A + (B + C) = (A + B) + C
Additive identity:
A + 0 = A
Where 0 is the zero matrix of the same dimension.
Additive inverse:
A + (−A) = O
The opposite matrix has each of its elements change sign.
Commutative:
A + B = B + A
Examples
Given the matrices:
Calculate:
A + B; A - B
