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

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:

Matrices

Calculate:

A + B;     A - B


Adding Matrices


Subtracting Matrices