Introduction:
Matrix multiplication is an important operation in linear algebra. It involves multiplying two matrices to obtain a new matrix. There are several properties associated with matrix multiplication, and in this response, we will discuss each property and explain why option 'D' is the correct answer.

Multiplication is not commutative in general:
Matrix multiplication is not commutative in general, which means that the order of multiplication matters. When two matrices A and B are multiplied, it is possible that AB ≠ BA. This property can be demonstrated with a simple example. Let's consider two matrices A and B:

A = [1 2]
[3 4]

B = [5 6]
[7 8]

When we multiply AB, we get:

AB = [1*5+2*7 1*6+2*8]
[3*5+4*7 3*6+4*8]

= [19 22]
[43 50]

On the other hand, when we multiply BA, we get:

BA = [5*1+6*3 5*2+6*4]
[7*1+8*3 7*2+8*4]

= [23 34]
[31 46]

As we can see, AB ≠ BA, which demonstrates that matrix multiplication is not commutative in general.

Multiplication is associative:
Matrix multiplication is associative, which means that when three matrices A, B, and C are multiplied, the order of multiplication does not matter. Mathematically, (AB)C = A(BC). This property can be proven by expanding the expressions of both sides and showing that they are equal.

Multiplication is distributive over addition:
Matrix multiplication is distributive over addition, which means that when we have three matrices A, B, and C, and we multiply A by the sum of B and C, it is the same as multiplying A by B and then adding the result to A multiplied by C. Mathematically, A(B + C) = AB + AC. This property is also proven by expanding the expressions and showing their equality.

Conclusion:
In conclusion, matrix multiplication has various properties associated with it. While it is not commutative in general, it is associative and distributive over addition. Therefore, option 'D' is the correct answer as all of the mentioned properties are true for matrix multiplication. These properties play a crucial role in various applications of matrix algebra, such as solving systems of linear equations, transformations, and more.