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You can add and subtract the matrix of the same size as a resulting you get the matrix of the same size.

Definition.
Addition of matrix (sum of matrix) A + B is operation of a finding of a matrix C, entry of which are equal to the sum of all corresponding entry of matrix A and B, can be defined as:

сij = aij + bij

Definition.
Subtraction of matrix (difference of matrix) A - B is operation of a finding of a matrix C, entry of which are equal to a difference of all corresponding entry of matrix A and B, can be defined as:

сij = aij - bij

## Properties of matrix addition and subtraction

• Associativity: (A + B) + C = A + (B + C)
• A + Θ = Θ + A = A, where Θ - zero matrix
• A - A = Θ
• Commutativity: A + B = B + A

## Examples of matrix addition and subtraction

Example 1.
 Find the sum of matrices A = 4 2 and B = 3 1 . 9 0 -3 4

Solution:

 A + B = 4 2 + 3 1 = 4 + 3 2 + 1 = 7 3 9 0 -3 4 9 + (-3) 0 + 4 6 4
Example 2
 Find the difference of matrices A = 4 2 and B = 3 1 . 9 0 -3 4

Solution:

 A - B = 4 2 - 3 1 = 4 - 3 2 - 1 = 1 1 9 0 -3 4 9 - (-3) 0 - 4 12 -4
Example 3
 Find the matrix С = 2A + 3B, if A = 4 2 and B = 3 1 . 9 0 -3 4 4 -6 9 1

Solution:

 C = 2A + 3B = 2 4 2 + 3 3 1 = 2·4 + 3·3 2·2 + 3·1 = 17 7 9 0 -3 4 2·9 + 3·(-3) 2·0 + 3·4 9 12 4 -6 9 1 2·4 + 3·9 2·(-6) + 3·1 35 -9