Question

What are the properties of matrix multiplication?

Answer 1

The properties of matrix multiplication:

Matrix multiplication is a product of two matrices that produce a single matrix.

For the matrices $A,B$ and $C$

• Associative property: $A\left(BC\right)=\left(AB\right)C$
• Distributive property: $A\left(B+C\right)=AB+AC$
• Multiplicative identity: $AI=IA=A$, where $I$ is an identity matrix
• Multiplicative property of zero: $A0=0A=0$