I can multiple matricies in any order? I am trying to complete some fairly simple matrix algebra for a homework task. 

Is it possible to multiple matrices in any order? 

Is the method for the below correct?

Thanks
In general, for matrices $A$ and $B$,
$$AB \neq BA,$$
so we can't change the order of the matrices in an expression. However,
$$(AB)C=A(BC)=ABC,$$
so we can perform the multiplication operations in any order.

This is because we can remove all the brackets from the expression for a sequence of multiplications by repeatedly applying the rule. For example:

$$(A((BC)(DE)))F$$
$$=A((BC)(DE))F$$
$$=A(BC)(DE)F$$
$$=ABC(DE)F$$
$$=ABCDEF$$

However the terms were originally grouped, we end up with $ABCDEF$.
The algebraic explanation is that the set of $n\times n$-matrices $M_n(R)$ over a commutative ring $R$ (entries) forms a ring with unity (unit matrix). This includes that the multiplicative monoid is associative, i.e.,
$A(BC) = (AB)C$ for any matrices $A,B,C\in M_n(R)$.