( -1, 3)^{T} **·** ( 2, 4 )^{T} = -1*2 + 3*4 = -2 + 12 = 10

( 2, 4 )^{T} **·** ( -1, 3)^{T} = 2*(-1) + 4*3 = -2 + 12 = 10

The dot product of column matrices is commutative:

a · b=b · a

As with the dot product of vectors, the order of operands makes no difference.
Write out the definition of dot product for both arrangements of
**a** and **b**:

a · b= ( a_{1}, a_{2})^{T}·( b_{1}, b_{2})^{T}= a_{1}b_{1}+ a_{2}b_{2}

b · a= ( b_{1}, b_{2})^{T}·( a_{1}, a_{2})^{T}= b_{1}a_{1}+ b_{2}a_{2}= a_{1}b_{1}+ a_{2}b_{2}

(Just in case your eyes have glazed over: notice that the stuff after the last "=" sign is the same in each case.)

(Review: ) What do you think might be true about:

a · b · c