Matrix addition is both associative and commutative.

Associativity of Matrix Addition:
The addition of matrices is associative, which means that the grouping of the matrices being added does not affect the final result. In other words, when adding three or more matrices together, the order in which the additions are performed does not matter.

For example, let's consider three matrices A, B, and C. Their addition can be represented as:
(A + B) + C = D
A + (B + C) = E

According to the associativity property, matrices D and E will be equal, regardless of the order in which the additions are performed.

Commutativity of Matrix Addition:
The addition of matrices is also commutative, which means that the order in which the matrices are added does not affect the final result.

For example, let's consider two matrices A and B. Their addition can be represented as:
A + B = F
B + A = G

According to the commutativity property, matrices F and G will be equal, regardless of the order in which the matrices are added.

Explanation:
To further clarify the properties of matrix addition, let's take an example with actual matrices. Consider the following matrices:

A = [1 2]
[3 4]

B = [5 6]
[7 8]

C = [9 10]
[11 12]

Now let's perform the operations to demonstrate the properties:

Associativity:
(A + B) + C = ([1 2] + [5 6]) + [9 10] = [6 8] + [9 10] = [15 18]
[20 22]
A + (B + C) = [1 2] + ([5 6] + [9 10]) = [1 2] + [14 16] = [15 18]
[20 22]

As we can see, regardless of the grouping of the additions, the result is the same.

Commutativity:
A + B = [1 2] + [5 6] = [6 8]
[8 10]

B + A = [5 6] + [1 2] = [6 8]
[8 10]

The result is the same regardless of the order in which the matrices are added.

Therefore, matrix addition is both associative and commutative.