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Distributive property:
1. Distributive property of scalar and two matrices - $$p(A+B) = pA+ pB$$

Let $$A$$, and $$B$$ be $$m×n$$ matrices and $$p$$ and $$q$$ be two non-zero scalars (numbers).
Example:
Consider the matrices $$A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, B = \begin{bmatrix} 5 & 6\\ 7 & 8 \end{bmatrix}$$ and $$p = 2$$ then verify $$p(A+B) = pA+ pB$$.

Solution:

2. Distributive property of two scalars with a matrix - $$(p +q)A = pA +qA$$
Example:
Let's take the same matrices to prove $$A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$ to prove $$(p +q)A = pA +qA$$. Where $$p = 2$$ , and $$q = 4$$.

Solution: