The commutative law for scalar-matrix multiplication states that: s A = A s
And the associative law for matrix multiplication states that: (AB)C = A(BC)
Finally the dot product of two column vectors states that: a$\cdot$b = a$^T$b
Using the above rules are we allowed to manipulate an equation as such: (a$\cdot$b)c = c(a$^T$b) = (c a$^T$)b where a, b and c are column vectors.
Specifically we use the commutative scalar-matrix rule to change the order in which we multiply by c, but in doing so we are no longer creating a scalar from a $\cdot$ b, so does the scalar-matrix rule still hold?