# Adding Matrices

Given two matrices of the same dimension, **A = (a _{ij})** and

**B = (b**, the matrix sum is defined as:

_{ij})**A + B = (a**. That is, the resultant matrix's elements are obtained by adding the elements of the two matrices that occupy the same position.

_{ij}+ b_{ij})## 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**

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