Matrix multiplication, rules

Summary

• \(A,B,C\) are matrices with dimensions such that the products below are defined. \(α\) is a scalar.
• \(AB\) is not necessarily equal to \(BA\) (commutative law does not hold for matrix multiplication)
• \((AB)C=A(BC)\) (the associative law holds for matrix multiplication)
• \(A(B+C)=AB+AC\) (the distributive law holds for matrices)
• \((A+B)C=AC+BC\)
• \(α(AB)=(αA)B=A(αB)\)
• \(AI=IA=A\) where \(I\) is the identity matrix
• \((AB)^T=B^TA^T\)