Associative Law for Matrices

The associative law simply states that parentheses can be moved around in Matrix Multiplication such that

$$E(AB)=(EA)B$$

Splitting Colums

Therefore it is also true that if $E$ and $A$ are both matrices with multiple columns in the relation

$$AB$$

We can split this operation into multiplication of the separate columns with each other. When the columns of $B$ are $b\_1,\dots ,b\_n$ and $A$ has $a\_1,\dots ,a\_n$ then this holds.

$$AB=A\text{[}b\_1\dots b\_n]=Ab\_1\dots Ab\_2$$