Let $A,B,C$ be matrices of appropriate sizes so that all of the following operations can be performed. Let $\alpha \in \mathbb{R}$ be any scalar. Then, all of the following are algebraic properties of matrix-matrix multiplication.

1. Associativity: $(AB)C=A(BC)$
2. Left distributivity: $A(B\pm C)=AB\pm AC$
3. Right distributivity: $(A\pm B)C=AC\pm BC$
4. Identity Matrix: $AI=A=IA$
5. Zero Matrix: $A0=0=0A$
6. Transpose: $(AB{)}^T=B^T{A}^T$
7. Scalar Multiplication: $(\alpha A)B=A(\alpha B)$