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.

Adding Matrices

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

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.


A + B = B + A


Given the matrices:



A + B;     A - B

Adding Matrices

Subtracting Matrices