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
The sum of two matrices of dimension m x n is another matix of dimension m x n.
A + (B + C) = (A + B) + C
A + 0 = A
Where 0 is the zero matrix of the same dimension.
A + (−A) = O
The opposite matrix has each of its elements change sign.
A + B = B + A
Given the matrices:
A + B; A - B